Persons: Matveev, Sergei Vladimirovich

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Matveev, Sergei Vladimirovich

Total publications:	107 (96)
in MathSciNet:	84 (83)
in zbMATH:	66 (66)
in Web of Science:	45 (42)
in Scopus:	48 (47)
Cited articles:	54
Citations:	931
Presentations:	4

Number of views:
This page:	9059
Abstract pages:	20130
Full texts:	6330
References:	1656

Member of the Russian Academy of Sciences

Professor

Doctor of physico-mathematical sciences (1988)

Speciality:

01.01.04 (Geometry and topology)

Birth date:

5.12.1947

E-mail:

Keywords:

manifold; 3-manifold; algorithmic recognition; complexity theory, classification.

Subject:

The theory of elementary moves on special polyhedra is elaborated. It is proved that the restriction of the Zeeman conjecture onto special polyhedra is equivalent to the union of the Poincare conjecture and the Andrews–Curtis conjecture. Complexity theory of 3-manifolds is constructed and all the manifolds up to complexity 8 are classified. A closed hyperbolic 3-manifold of the smallest complexity is constructed. It has the smallest known volume. A complete proof of the algorithmic classification theorem for sufficiently large 3-manifolds is written.

Biography

Graduated from Faculty of Mathematics and Mechanics of Moscow State University in 1970. Ph.D. thesis was awarded in 1970. D.Sci. thesis was awarded in 1988. Have more than 50 published papers.

Corresponding member of Petrov academy of sciences and arts.

Main publications:

Matveev S., Rolfsen D. Spines and embeddings of $n$-manifolds // J. London Math. Soc. (2). V. 59. 1999. P. 359–368.
Matveev S. Computer classification of 3-manifolds // Russian Journal of Mathematical Physics. V. 7, no. 3. 2000. P. 319–329.

https://www.mathnet.ru/eng/person8625

https://scholar.google.com/citations?user=lJEn1GIAAAAJ&hl=en

https://zbmath.org/authors/ai:matveev.sergei-vladimirovich

https://mathscinet.ams.org/mathscinet/MRAuthorID/225371

https://elibrary.ru/author_items.asp?authorid=4672

https://www.webofscience.com/wos/author/record/J-5948-2013

https://www.scopus.com/authid/detail.url?authorId=16407484100

Full list of publications:

scientific publications

		Citations (Crossref Cited-By Service + Math-Net.Ru)


2020
1.	S. V. Matveev, V. V. Tarkaev, “Recognition and tabulation of $3$-manifolds up to complexity $13$”, Chebyshevskii sb., 21:2 (2020), 290–300 ;

2019
2.	S. V. Matveev, “An example of the decomposition non-uniqueness for a 3-dimensional geometric object”, Chelyab. Fiz.-Mat. Zh., 4:3 (2019), 265–275

2018
3.	A. Yu. Vesnin, S. V. Matveev, E. A. Fominykh, “New aspects of complexity theory for 3-manifolds”, Russian Math. Surveys, 73:4 (2018), 615–660

2017
4.	S. King, S. Matveev, V. Tarkaev, V. Turaev, “Dijkgraaf-Witten $Z_2$-invariants for Seifert manifolds”, Journal of Knot Theory and Its Ramifications, 26:1 (2017), 1750006 , 7 pp.

2018
5.	A. A. Akimova, S. V. Matveev, V. V. Tarkaev, “Classification of links of small complexity in a thickened torus”, Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), 12–24

2017
6.	J. Glock, C. Hog-Angeloni, S. Matveev, “2-Complexes and 3-Manifolds”, Advances in Two-Dimensional Homotopy and Combinatorial Group Theory, London Mathematical Society Lecture Note Series, eds. W. Metzler, S. Rosebrock, Cambridge University Press, Cambridge, 2017, 103–127

2016
7.	S. V. Matveev, L. R. Nabeeva, “Tabulating knots in the thickened Klein bottle”, Siberian Mathematical Journal, 57:3 (2016), 542–548

2015
8.	S. V. Matveev, V. G. Turaev, “Dijkgraaf-Witten Invariants over $Z_2$ for 3-Manifolds”, Doklady Mathematics, 91:1 (2015), 9–11
9.	S. V. Matveev, “Mnogomernye mnogoobraziya i ob'edineniya vokselei”, Trudy Chetvertoi Mezhdunarodnoi nauchnoi konferentsii “Informatsionnye tekhnologii i sistemy” (Bannoe, 25 fevralya–1 marta 2015 g.), eds. Yu.S. Popkov, A.V. Melnikov, Chelyabinskii gosudarstvennyi universitet, Chelyabinsk, 2015, 19

2014
10.	A. A. Akimova, S. V. Matveev, “Classification of genus 1 virtual knots having at most five classical crossings”, Journal of Knot Theory and Its Ramifications, 23:6 (2014), 1450031 , 19 pp.	13 ^[x]
11.	S. V. Matveev, D. O. Nikolaev, “The structure of 3-manifolds of complexity zero”, Doklady Mathematics, 89:2 (2014), 143–145
12.	S. V. Matveev, “Zadanie trekhmernykh ob'ektov v pamyati kompyutera”, Trudy Tretei mezhdunarodnoi nauchnoi konferentsii “Informatsionnye tekhnologii i sistemy” (Bannoe, 26 fevralya–2 marta 2014 g.), eds. Yu.S. Popkov, A.V. Melnikov, Chelyabinskii gosudarstvennyi universitet, Chelyabinsk, 2014, 38–39

2013
13.	S. V. Matveev, A. V. Chernavskii, “O teoreme L.V. Keldysh i mnogokanalnoi svyazi”, Trudy Vtoroi mezhdunarodnoi nauchnoi konferentsii “Informatsionnye tekhnologii i sistemy” (Bannoe, 27 fevralya–3 marta 2013 g.), eds. A.V. Melnikov, Chelyabinskii gosudarstvennyi universitet, Chelyabinsk, 2013, 9–10

2012
14.	S. V. Matveev, “Roots and decompositions of three-dimensional topological objects”, Russian Mathematical Surveys, 67:3 (2012), 459–507
15.	S. V. Matveev, “Moves on special spines”, Vestnik Chelyabinskogo gosudarstvennogo universiteta, 2012, no. 15, 129–133

2014
16.	A. A. Akimova, S. V. Matveev, “Classification of Knots of Small Complexity in Thickened Tori”, Journal of Mathematical Sciences, 202:1 (2014), 1–12

2012
17.	S. V. Matveev, “Prime decompositions of knots in $T^{2}\times I$”, Topology and its Applications, 159:7 (2012), 1820–1824	10 ^[x]
18.	S. V. Matveev, “Kompyuternoe predstavlenie trekhmernykh mnogoobrazii i vokselnye izobrazheniya”, Materialy Pervoi Mezhdunarodnoi konferentsii “Informatsionnye tekhnologii i sistemy” (Bannoe, 28 fevralya–4 marta 2012 g.), eds. V. A. Melnikov, Chelyabinskii gosudarstvennyi universitet, Chelyabinsk, 2012, 16–19
19.	P. Korablev, S. Matveev, “Five lectures on 3-manifold topology”, Strasbourg Master Class on Geometry, IRMA Lectures in Mathematics and Theoretical Physics, 18, eds. A. Papadopoulos, European Mathematical Society, Zurich, 2012, 255–284
20.	S. V. Matveev, “Kompyuternoe tabulirovanie trekhmernykh mnogoobrazii”, First Yaroslavl Summer School on Discrete and Computational Geometry. Lecture Notes, Delaunay Library, 1, Yaroslavl State University, Yaroslavl, 2012, 147–163

2011
21.	S. Matveev, V. Turaev, “A semigroup of theta-curves in 3-manifolds”, Moscow Mathematical Journal, 11:4 (2011), 805–814	9 ^[x]
22.	A. Yu. Vesnin, S. V. Matveev, E. A. Fominykh, “Complexity of 3-dimensional manifolds: exact values and estimates”, Siberian Electronic Mathematical Reports, 8 (2011), 341–364
23.	F. G. Korablev, S. V. Matveev, “Reduction of knots in thickened surfaces and virtual knots”, Doklady Mathematics, 83:2 (2011), 262–264
24.	S. V. Matveev, “On prime decompositions of knots in thickened surfaces”, Bulletin of Kemerovo State University, 2011, 67–72

2010
25.	S. V. Matveev, “Decomposition of homologically trivial knots in $F\times I$”, Doklady Mathematics, 82:1 (2010), 511–513

2009
26.	S. Matveev, M. Polyak, “A simple formula for the Casson-Walker invariant”, Journal of Knot Theory and Its Ramifications, 18:6 (2009), 841–864	4 ^[x]
27.	S. Matveev, C. Petronio, A. Vesnin, “Two-sided asymptotic bounds for the complexity of some closed hyperbolic three-manifolds”, Journal of the Australian Mathematical Society, 86:2 (2009), 205–219	22 ^[x]
28.	F. G. Korablëv, S. V. Matveev, V. V. Tarkaev, “O trekhmernykh mnogoobraziyakh roda 2”, Vestnik Chelyabinskogo gosudarstvennogo universiteta. Matematika, mekhanika, informatika, 2009, no. 20, 105–121
29.	S. V. Matveev, “Virtual 3-manifolds”, Siberian Electronic Mathematical Reports, 6 (2009), 518–521
30.	F. G. Korablev, S. V. Matveev, V. V. Tarkaev, Vestnik Chelyabinsk. Gos. Univ., 2009, no. 11, 105–121

2008
31.	C. Hog-Angeloni, S. Matveev, “Roots in 3-manifold topology”, Geometry & Topology Monographs, 14 (2008), 295–319	10 ^[x]

2007
32.	A. Yu. Vesnin, S. V. Matveev, C. Petronio, “Two-sided complexity bounds for Löbell manifolds”, Doklady Mathematics, 76:2 (2007), 689–691
33.	S. V. Matveev, Algoritmicheskaya topologiya i klassifikatsiya trekhmernykh mnogoobrazii, Moskovskii tsentr nepreryvnogo matematicheskogo obrazovaniya, Moskva, 2007 , 456 pp.
34.	S. Matveev, Algorithmic Topology and Classification of 3-Manifolds, Algorithms and Computation in Mathematics, 9, Second Edition, Springer, Berlin, Heidelberg, 2007 , xiv+492 pp.	12 ^[x]

2005
35.	S. V. Matveev, “Tabulation of three-dimensional manifolds”, Russian Mathematical Surveys, 60:4 (2005), 673–698
36.	S. V. Matveev, “Recognition and tabulation of 3-manifolds”, Doklady Mathematics, 71:1 (2005), 20–22

2004
37.	S. Matveev, A. Perfilyev, “Periodicity of the degrees of maps between seifert manifolds”, Doklady Mathematics, 69:2 (2004), 225–227

2003
38.	S. Matveev, M. Polyak, “Finite-type invariants of cubic complexes”, Acta Applicandae Mathematicae, 75:1-3 (2003), 125–132	7 ^[x]
39.	S. Matveev, Algorithmic Topology and Classification of 3-Manifolds, Algorithms and Computation in Mathematics, 9, Springer, Berlin, Heidelberg, 2003 , xii+478 pp.	77 ^[x]

2006
40.	S. V. Matveev, Lectures on Algebraic Topology, EMS Series of Lectures in Mathematics, 3, European Mathematical Society, Zurich, 2006 , viii+99 pp.

2003
41.	S. V. Matveev, V. V. Tarkaev, “Kompyuternaya klassifikatsiya rasshirennykh diagramm khegora”, Vestnik Chelyabinskogo universiteta. Seriya 3. Matematika, mekhanika, informatika, 2(8) (2003), 146–152
42.	S. V. Matveev, V. V. Tarkaev, Vestnik Chelyabinsk. Gos. Univ., 2003, no. 8, 146–152

2002
43.	S. V. Matveev, E. A. Fominykh, “Normal surfaces in 3-manifolds”, Doklady Mathematics, 65:3 (2002), 429–432
44.	S. Matveev, M. Polyak, “Cubic complexes and finite type invariants”, Geometry & Topology Monographs, 4 (2002), 215–233	5 ^[x]

2001
45.	S. V. Matveev, E. L. Pervova, “Lower bounds on the complexity of three-dimensional manifolds”, Doklady Mathematics, 63:3 (2001), 314–315
46.	S. V. Matveev, “Algorithmic classification of 3-manifolds and knots”, Gazette des Mathematiciens, 89 (2001), 49–61
47.	C. Hayat-Legrand, S. Matveev, H. Zieschang, “Computer calculation of the degree of maps into the Poincare homology sphere”, Experimental Mathematics, 10:4 (2001), 497–508	4 ^[x]
48.	S. V. Matveev, “On invariants of Turaev-Viro type”, Atti del Seminario matematico e fisico dell'Università di Modena, 49 (2001), 155–166

2003
49.	S. V. Matveev, “Complexity of three-dimensional manifolds”, Proceedings of the Conference “Geometry and Applications" dedicated to the seventieth birthday of V. A. Toponogov, Siberian Advances in Mathematics, 13, no. 3, 2003

2001
50.	S. Matveev, “Computer Presentation of 3-Manifolds”, Digital and Image Geometry, Advanced Lectures, Lecture Notes in Computer Science, 2243, Springer, Berlin, Heidelberg, 2001, 59–74

2000
51.	S. V. Matveev, “Computer classification of 3-manifolds”, Russian Journal of Mathematical Physics, 7:3 (2000), 319–329
52.	S. Matveev, A. Oshemkov, A. Tuzhilin, “On a topological obstruction for constructing hyperbolic structures”, Proceedings of the International Conference “Low-dimensional topology and combinatorial group theory” (Chelyabinsk, 31 july – 7 august 1999), Institute of Mathematics NAS of Ukraine, Kiev, 2000, 227–233

2003
53.	S. V. Matveev, M. A. Ovchinnikov, M. V. Sokolov, “Construction and properties of the $t$-invariant”, Journal of Mathematical Sciences, 113:6 (2003), 849–855

1999
54.	S. V. Matveev, “Algorithmic Classification of 3-Manifolds: Problems and Results”, Proceedings of the Steklov Institute of Mathematics, 225 (1999), 250–260
55.	S. Matveev, D. Rolfsen, “Spines and embeddings of $n$-manifolds”, Journal of the London Mathematical Society, 59:1 (1999), 359–368

1998
56.	S. V. Matveev, “Generalized graph manifolds and their effective recognition”, Sbornik: Mathematics, 189:10 (1998), 1517–1531
57.	S. V. Matveev, “Computer recognition of three-manifolds”, Experimental Mathematics, 7:2 (1998), 153–161	9 ^[x]
58.	S. V. Matveev, A. T. Fomenko, Algoritmicheskie i kompyuternye metody v trekhmernoi topologii, Kibernetika – neogranichennye vozmozhnosti i vozmozhnye ogranicheniya, vtoroe izdanie, Nauka, Moskva, 1998 , 302 pp.

1997
59.	S. V. Matveev, “Classification of sufficiently large three-dimensional manifolds”, Russian Mathematical Surveys, 52:5 (1997), 1029–1055
60.	S. V. Matveev, “On the recognition problem for Haken 3-manifolds”, The proceedings of the Workshop on Differential Geometry and Topology (Palermo (Italy), June 3–9, 1996), Supplemento ai Rendiconti del Circolo Matematico di Palermo, 49, no. 2, 1997, 131–148
61.	A. T. Fomenko, S. V. Matveev, Algorithmic and Computer Methods for Three-Manifolds, Mathematics and Its Applications, 425, Springer Science+Business Media, Dordrecht, 1997 , xii+337 pp.	60 ^[x]

1999
62.	S. V. Matveev, M. V. Sokolov, “On a simple invariant of Turaev-Viro type”, Journal of Mathematical Sciences, 94:2 (1999), 1226–1229

1995
63.	S. V. Matveev, “An algorithm for the recognition of 3-spheres (according to Thompson)”, Sbornik: Mathematics, 186:5 (1995), 695–710

1994
64.	S. Matveev, M. Polyak, “On a tangle presentation of the mapping class groups of surfaces”, Contemporary Mathematics, 164 (1994), 219–229	1 ^[x]
65.	S. Matveev, M. Polyak, “A geometrical presentation of the surface mapping class group and surgery”, Communications in Mathematical Physics, 160:3 (1994), 537–550	12 ^[x]
66.	D. Gillman, S. Matveev, D. Rolfsen, “Collapsing and reconstruction of manifolds”, Contemporary Mathematics, 164 (1994), 35–39	3 ^[x]
67.	S. V. Matveev, T. Nowik, “On 3-Manifolds having the same Turaev-Viro invariants”, Russian Journal of Mathematical Physics, 2:3 (1994), 317–324

1995
68.	S. V. Matveev, “Three-manifolds. Classical results”, Journal of Mathematical Sciences, 74:1 (1995), 834–860

1993
69.	S. Matveev, D. Rolfsen, “Zeeman's collapsing conjecture”, Two-dimensional homotopy and combinatorial group theory, London Mathematical Society Lecture Note Series, 197, Cambridge University Press, 1993, 335–364	3 ^[x]

1991
70.	S. V. Matveev, A. T. Fomenko, Algoritmicheskie i kompyuternye metody v trekhmernoi topologii, Moskovskii gosudarstvennyi universitet im. M.V. Lomonosova, Moskva, 1991 , 301 pp.

1990
71.	A. V. Bolsinov, S. V. Matveev, A. T. Fomenko, “Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity”, Russian Mathematical Surveys, 45:2 (1990), 59–94
72.	S. V. Matveev, “Complexity theory of three-dimensional manifolds”, Acta Applicandae Mathematicae, 19:2 (1990), 101–130	69 ^[x]

1989
73.	S. V. Matveev, “Additivity of complexity and Haken’s method in the topology of three-dimensional manifolds”, Ukrainian Mathematical Journal, 41:9 (1989), 1063–1068

1988
74.	S. V. Matveev, A. T. Fomenko, “Morse-type theory for integrable Hamiltonian systems with tame integrals”, Mathematical notes of the Academy of Sciences of the USSR, 43:5 (1988), 382–386
75.	S. V. Matveev, A. T. Fomenko, “Constant energy surfaces of Hamiltonian systems, enumeration of three-dimensional manifolds in increasing order of complexity, and computation of volumes of closed hyperbolic manifolds”, Russian Mathematical Surveys, 43:1 (1988), 3–24

1989
76.	S. V. Matveev, A. T. Fomenko, V. V. Sharko, “Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems”, Mathematics of the USSR-Sbornik, 63:2 (1989), 319–336
77.	S. V. Matveev, “Complexity of three-dimensional manifolds and their enumeration in the order of increasing complexity”, Soviet Mathematics. Doklady, 38:1 (1989), 75–78

1988
78.	S. V. Matveev, “Slozhnost geometricheskikh mnogoobrazii”, Sbornik nauchnykh trudov “Nekotorye voprosy analiza i differentsialnoi topologii”, Institut matematiki Akademii nauk USSR, 1988, 48–55
79.	S. V. Matveev, Teoriya slozhnosti trekhmernykh mnogoobrazii, Preprint № 88.13, Institut matematiki Akademii nauk USSR, Kiev, 1988 , 32 pp.
80.	S. V. Matveev, Spetsialnye spainy i teoriya slozhnosti 3-mnogoobrazii, dissertatsiya na soiskanie uchenoi stepeni doktora fiziko-matematicheskikh nauk, MGU, Moskva, 1988 , 300 pp.
81.	S. V. Matveev, “Transformations of special spines and the Zeeman conjecture”, Mathematics of the USSR-Izvestiya, 31:2 (1988), 423–434

1987
82.	S. V. Matveev, “Generalized surgery of three-dimensional manifolds and representations of homology spheres”, Mathematical notes of the Academy of Sciences of the USSR, 42:2 (1987), 651–656
83.	S. V. Matveev, “Universal 3-deformations of special polyhedra”, Russian Mathematical Surveys, 42:3 (1987), 226–227
84.	S. V. Matveev, “Zeeman's conjecture for unthickened special polyhedra is equivalent to the Andrews-Curtis conjecture”, Siberian Mathematical Journal, 28:6 (1987), 917–928
85.	S. V. Matveev, “Structure of the second homotopy group of the union of two spaces”, Journal of Soviet Mathematics, 37:3 (1987), 1135–1141

1984
86.	S. V. Matveev, Algebraicheskaya topologiya: metodicheskie ukazaniya, Chelyabinskii gosudarstvennyi universitet, Chelyabinsk, 1984 , 24 pp.
87.	S. V. Matveev, “Distributive groupoids in knot theory”, Mathematics of the USSR-Sbornik, 47:1 (1984), 73–83

1981
88.	A. L. Zil'berg, S. V. Matveev, “Relations in the homeotropy group of a complete pretzel and the group of plat braids”, Mathematical notes of the Academy of Sciences of the USSR, 29:4 (1981), 290–295

1980
89.	S. V. Matveev, “Trekhmernye mnogoobraziya, skonstruirovannye na zamknutykh tsepochkakh”, Prikladnaya matematika. Tematicheskii sbornik nauchnykh trudov, 252, Chelyabinskii politekhnicheskii institut, Chelyabinsk, 1980, 79–82

1975
90.	S. V. Matveev, “Odin sposob zadaniya 3-mnogoobrazii”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika., 1975, no. 3, 11–20
91.	A. V. Chernavskii, S. V. Matveev, Sovremennaya topologiya mnogoobrazii, Voronezhskii gosudarstvennyi universitet, Voronezh, 1975 , 70 pp.

1974
92.	S. V. Matveev, V. V. Savvateev, “Trekhmernye mnogoobraziya, imeyuschie prostye spetsialnye ostovy”, Colloquium Mathematicum, 32:1 (1974), 83–97	5 ^[x]
93.	A. V. Chernavskii,S. V. Matveev, Osnovy topologii mnogoobrazii, Nauchnye trudy, 192, Kubanskii gosudarstvennyi universitet, Krasnodar, 1974 , 176 pp.

1973
94.	S. V. Matveev, “Special spines of piecewise linear manifolds”, Mathematics of the USSR-Sbornik, 21:2 (1973), 279–291
95.	S. V. Matveev, Spetsialnye spainy kusochno-lineinykh mnogoobrazii, dissertatsiya na soiskanie uchenoi stepeni kandidata fiziko-matematicheskikh nauk, MGU, Moskva, 1973 , 88 pp.

1972
96.	S. V. Matveev, “Approksimatsiya vlozhenii mnogoobrazii lokalno ploskimi v korazmernosti bolshe dvukh”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika., 1972, no. 6, 53–57

Presentations in Math-Net.Ru

1.	[Short address on the occasion of A. V. Chernavsky's 85th birthday] S. V. Matveev Geometric Topology Seminar February 22, 2023 14:00
2.	New aspects of complexity theory for $3$-manifolds Sergei V. Matveev International conference "Algebraic Topology, Combinatorics, and Mathematical Physics" on occasion of Victor Buchstaber's 75th birthday May 26, 2018 10:00
3.	Лемма о Диаманте и примарные разложения топологических объектов S. V. Matveev Steklov Mathematical Institute Seminar October 20, 2016 16:00
4.	Decompositions of global knots S. V. Matveev P.K. Rashevskii seminar on tensor and vector analysis with applications in geometry, mechanics and physics October 8, 2012 18:30

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