combinatorial manifold,
triangulation,
Pontryagin classes,
problem of realisation of cycles,
simplicial complex,
simple polytope,
permutohedron,
flexible polyhedron,
the bellows conjecture.
Combinatorial topology, algebraic topology, characteristic classes, problem on realization of cycles, combinatorial geometry, flexible polyhedra.
Main publications:
Alexander A. Gaifullin, “Configuration spaces, bistellar moves, and combinatorial formulae for the first Pontryagin class”, Proc. Steklov Inst. Math., 268 (2010), 70–86 , arXiv: 0912.3933
A. A. Gaifullin, “The construction of combinatorial manifolds with prescribed sets of links of vertices”, Izv. Math., 72:5 (2008), 845–899 , arXiv: 0801.4741
A. A. Gaifullin, “The Manifold of Isospectral Symmetric Tridiagonal Matrices and Realization of Cycles by Aspherical Manifolds”, Proc. Steklov Inst. Math., 263 (2008), 38–56
A. A. Gaifullin, “Computation of characteristic classes of a manifold from a triangulation of it”, Russian Math. Surveys, 60:4 (2005), 615–644
A. A. Gaifullin, “Local formulae for combinatorial Pontryagin classes”, Izv. Math., 68:5 (2004), 861–910 , arXiv: math/0407035
A. A. Gaifullin, “Generalization of Sabitov's theorem to polyhedra of arbitrary dimensions”, Discrete Comput. Geom., 52:2 (2014), 195–220 , arXiv: 1210.5408
A. A. Gaifullin, “Local formulae for combinatorial Pontryagin classes”, Izv. Math., 68:5 (2004), 861–910 , arXiv: math/0407035
6.
A. A. Gaifullin, “Embedded flexible spherical cross-polytopes with nonconstant volumes”, Proc. Steklov Inst. Math., 288 (2015), 56–80 , arXiv: 1501.06198
7.
A. A. Gaifullin, “The analytic continuation of volume and the Bellows conjecture in Lobachevsky spaces”, Sb. Math., 206:11 (2015), 1564–1609 , arXiv: 1504.02977
8.
A. A. Gaifullin, “Computation of characteristic classes of a manifold from a triangulation of it”, Russian Math. Surveys, 60:4 (2005), 615–644
9.
A. A. Gaifullin, “The construction of combinatorial manifolds with prescribed sets of links of vertices”, Izv. Math., 72:5 (2008), 845–899 , arXiv: 0801.4741
10.
A. A. Gaifullin, “Realisation of cycles by aspherical manifolds”, Russian Math. Surveys, 63:3 (2008), 562–564 , arXiv: 0806.3580
11.
A. A. Gaifullin, “The Manifold of Isospectral Symmetric Tridiagonal Matrices and Realization of Cycles by Aspherical Manifolds”, Proc. Steklov Inst. Math., 263 (2008), 38–56
12.
Alexander A. Gaifullin, “The bellows conjecture for small flexible polyhedra in non-Euclidean spaces”, Mosc. Math. J., 17:2 (2017), 269–290 , arXiv: 1605.04568
V. M. Buchstaber, A. P. Veselov, A. A. Gaifullin, “Classification of involutive commutative two-valued groups”, Russian Math. Surveys, 77:4 (2022), 651–727 , arXiv: 2302.05909
14.
Alexander A. Gaifullin, Leonid S. Ignashchenko, “Dehn invariant and scissors congruence of flexible polyhedra”, Proc. Steklov Inst. Math., 302 (2018), 130–145 , arXiv: 1710.11247
15.
Alexander A. Gaifullin, “Configuration spaces, bistellar moves, and combinatorial formulae for the first Pontryagin class”, Proc. Steklov Inst. Math., 268 (2010), 70–86 , arXiv: 0912.3933
16.
A. A. Gaifullin, “Explicit construction of manifolds realising prescribed homology classes”, Russian Math. Surveys, 62:6 (2007), 1199–1201 , arXiv: 0712.1709
17.
Alexander A. Gaifullin, “On the top homology group of the Johnson kernel”, Mosc. Math. J., 22:1 (2022), 83–102 , arXiv: 1903.03864;
A. A. Gaifullin, “On a spectral sequence for the action of the Torelli group of genus $3$ on the complex of cycles”, Izv. Math., 85:6 (2021), 1060–1127 , arXiv: 2011.00295
19.
A. A. Gaifullin, D. A. Gorodkov, “An explicit local combinatorial formula for the first Pontryagin class”, Russian Math. Surveys, 74:6 (2019), 1120–1122
20.
A. A. Gaifullin, “Small covers of graph-associahedra and realization of cycles”, Sb. Math., 207:11 (2016), 1537–1561 , arXiv: 1611.01816
21.
V. M. Buchstaber, A. A. Gaifullin, “Representations of $m$-valued groups on triangulations of manifolds”, Russian Math. Surveys, 61:3 (2006), 560–562
22.
A. A. Gaifullin, V. O. Manturov, “On the recognition of braids”, J. Knot Theory Ramifications, 11:8 (2002), 1193–1209
A. A. Gaifullin, “Combinatorial realisation of cycles and small covers”, European Congress of Mathematics (Kraków, 2–7 July, 2012), eds. R. Latala et al., European Mathematical Society, 2013, 315–330 , arXiv: 1204.0208
A. A. Gaifullin, P. V. Yagodovskii, “Integrability of $m$-valued dynamics by means of single-generated $m$-valued groups”, Russian Math. Surveys, 62:1 (2007), 181–183
25.
Izv. Math., 88:3 (2024), 419–467
26.
A. A. Gaifullin, “Commutativity of involutive two-valued groups”, Russian Math. Surveys, 79:2 (2024), 363–365 , arXiv: 2401.15191
27.
Alexander A. Gaifullin, Yury A. Neretin, “Infinite symmetric group, pseudomanifolds, and combinatorial cobordism-like structures”, J. Topol. Anal., 10:3 (2018), 605–625 , arXiv: 1501.04062
A. A. Gaifullin, “On an extension of the Birman–Craggs–Johnson homomorphism”, Russian Math. Surveys, 72:6 (2017), 1171–1173
29.
A. A. Gaifullin, S. A. Gaifullin, “Deformations of period lattices of flexible polyhedral surfaces”, Discrete Comput. Geom., 51:3 (2014), 650–665 , arXiv: 1306.0240
A. A. Gaifullin, “A Minimal Triangulation of Complex Projective Plane Admitting a Chess Colouring of Four-Dimensional Simplices”, Proc. Steklov Inst. Math., 266 (2009), 29–48 , arXiv: 0904.4222
A. A. Gaifullin, “On possible symmetry groups of 27-vertex triangulations of manifolds like the octonionic projective plane”, Sb. Math., 215:7 (2024), 869–910 , arXiv: 2310.16679
33.
A. A. Gaifullin, “On infinitely generated homology of Torelli groups”, Algebra i analiz, 35:6 (2023), 87–134 , arXiv: 1803.09311;
34.
A. A. Gaifullin, Flexible Polyhedra and Their Volumes, 2016 , 20 pp., arXiv: 1605.09316
35.
A. A. Gaifullin, “Problema realizatsii tsiklov i malye nakrytiya nad graf-assotsiedrami”, Aleksandrovskie chteniya. Tezisy dokladov (Moskva, 22–26 maya 2016 g.), Mekhaniko-matematicheskii f-t MGU, Moskva, 2016, 15
36.
A. A. Gaifullin, “Volumes of flexible polyhedra”, Tezisy Mezhdunarodnoi konferentsii “Dni geometrii v Novosibirske - 2014”, posvyaschënnoi 85-letiyu akademika Yuriya Grigorevicha Reshetnyaka (Novosibirsk, 24–27 sentyabrya 2014 g.), eds. I. A. Taimanov, A. Yu. Vesnin, Institut matematiki im. S. L. Soboleva SO RAN, Novosibirsk, 2014, 98–99
37.
A. A. Gaifullin, “Volume of a simplex as a multivalued algebraic function of the areas of its two-faces”, Topology, Geometry, Integrable Systems, and Mathematical Physics: Novikov's Seminar 2012–2014, Advances in the Mathematical Sciences, Amer. Math. Soc. Transl. Ser. 2, 234, eds. V. M. Buchstaber, B. A. Dubrovin, I. M. Krichever, Amer. Math. Soc., Providence, RI, 2014, 201–221 , arXiv: 1310.3417
A. A. Gaifullin, “Flexible polyhedra and their volumes”, Oberwolfach Rep., 11, no. 2, 2014, 1584–1586
40.
A. A. Gaifullin, “Coxeter groups, small covers, and realization of cycles”, International Open Chinese-Russian Conference “Torus Actions: Topology, Geometry and Number Theory”. Abstracts (Khabarovsk, 2–7 sentyabrya 2013 g.), Izdatelstvo TOGU, Khabarovsk, 2013, 35-36
41.
A. A. Gaifullin, “Flexible polyhedra and places of fields”, Yaroslavl International Conference “Geometry, Topology, and Applications”, September 23–27, 2013. Abstracts (Yaroslavl, 23–27 sentyabrya 2013 g.), Yaroslavskii gosudarstvennyi universitet im. P.G. Demidova, Yaroslavl, 2013, 53
42.
A. A. Gaifullin, “Combinatorial realisation of cycles and small covers”, 6th European Congress of Mathematics. Abstracts & Titles (Kraków, Poland, July 2–7, 2012), 6ECM, Kraków, 2012, 25–26
43.
A. A. Gaifullin, “Combinatorial realisation of cycles and simplicial volume”, Tezisy Mezhdunarodnoi konferentsii «Dni geometrii v Novosibirske, 2012», posvyaschënnoi 100-letiyu so dnya rozhdeniya akademika A.D. Aleksandrova (Novosibirsk, 30 avgusta – 1 sentyabrya 2012 g.), Institut matematiki im. S. L. Soboleva SO RAN, 2012, 12–13
44.
A. A. Gaifullin, “Sabitov Polynomials for Volumes of Four-dimensional Polyhedra”, The Fourth Geometry Meeting dedicated to the centenary of A. D. Alexandrov. Abstracts (Sankt-Peterburg, 20–24 avgusta 2012 g.), Izdatelstvo VVM, Sankt-Peterburg, 2012, 11
45.
A. A. Gaifullin, “Sabitov polynomials for volumes of four-dimensional polyhedra”, Yaroslavl International Conference “Discrete Geometry” dedicated to the centenary of A.D. Alexandrov. Abstracts (Yaroslavl, 13–18 avgusta 2012 g.), Yaroslavskii gosudarstvennyi universitet im. P.G. Demidova, Yaroslavl, 2012, 36–37
46.
A. A. Gaifullin, “Sabitov polynomials for polyhedra in four dimensions”, Mezhdunarodna konferentsiya «Toricheskaya topologiya i avtomorfnye funktsii». Tezisy dokladov (Moskva, 5–10 sentyabrya 2011 g.), Izdatelstvo TOGU, Khabarovsk, 2011, 27–35
47.
A. A. Gaifullin, “Sets of links of vertices of simplicial and cubic manifolds”, 2010 International Conference on Topology and its Applications. Abstracts (Nafpaktos, Greece, June 26–30, 2010), Technological Educational Institute of Messolonghi, Nafpaktos, 2010, 101–103
48.
A. A. Gaifullin, “Sets of links of vertices of triangulated manifolds and combinatorial approach to Steenrod’s problem on realisation of cycles”, Geometry, Topology, Algebra and Number Theory, Applications. The International Conference dedicated to the 120th anniversary of B.N. Delone. Abstracts (Moskva, 16–20 avgusta 2010 g.), Matematicheskii institut im. V.A. Steklova RAN, Moskovskii gosudarstvennyi universitet im. M.V. Lomonosova, Moskva, 2010, 11
49.
A. A. Gaifullin, Problema kombinatornogo vychisleniya ratsionalnykh klassov Pontryagina, Diss. … dokt. fiz.-matem. nauk, Matematicheskii institut im. V.A. Steklova RAN, Moskva, 2010 , 341 pp.
50.
A. A. Gaifullin, “Lokalnye kombinatornye formuly dlya klassov Pontryagina triangulirovannykh mnogoobrazii”, Differentsialnye uravneniya i topologiya: Mezhdunarodnaya konferentsiya, posvyaschennaya 100-letiyu so dnya rozhdeniya L.S. Pontryagina: Tezisy dokladov (Moskva, 17–22 iyunya 2008 g.), Izdatelskii otdel fakulteta VMiK MGU im. M.V. Lomonosova, 2008, 16
51.
A. A. Gaifullin, Kombinatornaya realizatsiya tsiklov, Diss. … kand. fiz.-matem. nauk, MGU im. M.V. Lomonosova, Mekhaniko-matematicheskii fakultet, Moskva, 2008 , 121 pp.
52.
A. A. Gaifullin, “On local formulae for combinatorial Pontryagin classes of manifolds”, Russian Math. Surveys, 59:2 (2004), 379–380
53.
A. A. Gaifullin, “Nerves of Coxeter groups”, Russian Math. Surveys, 58:3 (2003), 615–616
54.
A. A. Gaifullin, “Proektsii uzlov s edinstvennoi tochkoi mnogokratnogo transversalnogo samoperesecheniya”, Sovremennye issledovaniya v matematike i mekhanike, Trudy 23 Konferentsii molodykh uchenykh mekhaniko-matematicheskogo fakulteta MGU, Izd-vo TsPI pri mekh.-mat. fak. MGU, Moskva, 2001, 88–92
55.
A. A. Gaifullin, “New examples and partial classification of 15-vertex triangulations of the quaternionic projective plane”, Topology, Geometry, Combinatorics, and Mathematical Physics, Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 326, Steklov Math. Inst., Moscow, 2024
56.
N. Agakhanov, D. Belov, I. Bogdanov, A. Gaifullin, M. Grigor'ev, P. Kozhevnikov, O. Podlipsky, Kvant, 2019, no. 7, 40–43
57.
V. A. Alexandrov, L. D. Beklemishev, V. M. Buchstaber, A. Yu. Vesnin, A. A. Gaifullin, N. P. Dolbilin, N. Yu. Erokhovets, M. D. Kovalev, V. S. Makarov, S. P. Novikov, D. O. Orlov, A. N. Parshin, I. Kh. Sabitov, D. V. Treschev, O. K. Sheinman, E. V. Shchepin, “Mikhail Ivanovich Shtogrin (on his 80th birthday)”, Russian Math. Surveys, 74:6 (2019), 1159–1162
58.
N. H. Agakhanov, I. I. Bogdanov, A. A. Gaifullin, P. A. Kozhevnikov, Kvant, 2018, no. 8, 39–41
59.
A. A. Gaifullin, “Current algebras on Riemann surfaces: new results and applications (de Gruyter Expositions in Mathematics 58) By Oleg K. Sheinman”, Book review, Bull. London Math. Soc., 47:6 (2015), 1029–1032
60.
A. A. Gaifullin, A. V. Penskoi, S. V. Smirnov, Zadachi po lineinoi algebre i geometrii, MTsNMO, Moskva, 2014 , 152 pp. http://biblio.mccme.ru/node/5173
61.
A. M. Vershik, A. P. Veselov, A. A. Gaifullin, B. A. Dubrovin, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, D. V. Millionshchikov, S. P. Novikov, T. E. Panov, A. G. Sergeev, I. A. Taimanov, “Viktor Matveevich Buchstaber (on his 70th birthday)”, Russian Math. Surveys, 68:3 (2013), 581–590
62.
A. A. Gaifullin, T. E. Panov, “Victor Matveevich Buchstaber’s 70th birthday anniversary”, Trans. Moscow Math. Soc., 2013 (2013), 173
63.
Topologiya, geometriya, kombinatorika i matematicheskaya fizika, Sbornik statei. K 80-letiyu chlena-korrespondenta RAN Viktora Matveevicha Bukhshtabera, Trudy MIAN, 326, ed. A. A. Gaifullin, T. E. Panov, D. V. Gugnin, N. Yu. Erokhovets, MIAN, M., 2024
64.
Toricheskaya topologiya, deistviya grupp, geometriya i kombinatorika. Chast 1, Sbornik statei, Trudy MIAN, 317, ed. V. M. Bukhshtaber, A. A. Gaifullin, T. E. Panov, N. Yu. Erokhovets, MIAN, M., 2022 , 210 pp.
65.
Toricheskaya topologiya, deistviya grupp, geometriya i kombinatorika. Chast 2, Sbornik statei, Trudy MIAN, 318, ed. V. M. Bukhshtaber, A. A. Gaifullin, T. E. Panov, N. Yu. Erokhovets, MIAN, M., 2022 , 204 pp.
66.
Algebraicheskaya topologiya, kombinatorika i matematicheskaya fizika, Sbornik statei. K 75-letiyu so dnya rozhdeniya chlena-korrespondenta RAN Viktora Matveevicha Bukhshtabera, Trudy MIAN, 305, ed. S. P. Novikov, A. A. Gaifullin, T. E. Panov, A. A. Aizenberg, MIAN, M., 2019 , 374 pp.
Равносоставленность изгибаемых многогранников A. A. Gaifullin International conference "Discrete Mathematics and Mathematical Crystallography" dedicated to the 80th anniversary of Mikhail Ivanovich Stogrin September 26, 2018 16:00
Равносоставленность изгибаемых многогранников A. A. Gaifullin Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) November 22, 2017 18:30
Изгибаемые кросс-политопы и эллиптические функции Якоби A. A. Gaifullin Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) February 19, 2014 18:30
Геометрическое доказательство двух теорем Тома A. A. Gaifullin Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) January 19, 2011 14:00
Topology, Geometry, Combinatorics, and Mathematical Physics, Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 326, ed. A. A. Gaifullin, T. E. Panov, D. V. Gugnin, N. Yu. Erokhovets, 2024 http://mi.mathnet.ru/book1988
Toric Topology, Group Actions, Geometry, and Combinatorics. Part 1, Collected papers, Trudy Mat. Inst. Steklova, 317, ed. V. M. Buchstaber, A. A. Gaifullin, T. E. Panov, N. Yu. Erokhovets, 2022, 210 с. http://mi.mathnet.ru/book1902
Toric Topology, Group Actions, Geometry, and Combinatorics. Part 2, Collected papers, Trudy Mat. Inst. Steklova, 318, ed. V. M. Buchstaber, A. A. Gaifullin, T. E. Panov, N. Yu. Erokhovets, 2022, 204 с. http://mi.mathnet.ru/book1932
Algebraic topology, combinatorics, and mathematical physics, Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 75th birthday, Trudy Mat. Inst. Steklova, 305, ed. S. P. Novikov, A. A. Gaifullin, T. E. Panov, A. A. Ayzenberg, 2019, 374 с. http://mi.mathnet.ru/book1762