three-dimensional manifolds,
classification of manifolds,
normal surfaces,
crystallizations,
spines of manifolds,
efficient algorithms for recognising of knots and manifolds.
E. Fominykh, S. Garoufalidis, M. Goerner, V. Tarkaev, A. Vesnin, “A census of tetrahedral hyperbolic manifolds”, Experimental Mathematics, 25:4 (2016), 466–481
A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Complexity of virtual 3-manifolds”, Sb. Math., 207:11 (2016), 1493–1511
A.Yu. Vesnin, E.A. Fominykh, “Exact values of the complexity of Paoluzzi-Zimmermann manifolds”, Doklady Mathematics, 84:1 (2011), 542–544
E. Fominykh, B. Martelli, “$k$-normal surfaces”, Journal of Differential Geometry, 82:1 (2009), 101–114
D. D. Nigomedyanov, E. A. Fominykh, “$\beta_1$-triangulyatsii 3-mnogoobrazii”, Matematicheskie zametki (to appear)
2024
2.
A. V. Malyutin, E. A. Fominykh, “Faithful interpretations of Matveev's virtual manifolds”, Algebra i Analiz, 36:6 (2024), 82–111
2023
3.
D. D. Nigomedyanov, E. A. Fominykh, “A lower bound for triangulation complexity for compact 3-manifolds with boundary”, Russian Math. Surveys, 78:5 (2023), 955–957
2022
4.
Yu. S. Belousov, M. V. Karev, A. V. Malyutin, A. Yu. Miller, E. A. Fominykh, “Lernaean knots and band surgery”, St. Petersburg Math. J., 33:1 (2022), 23–46
2021
5.
E. A. Fominykh, E. V. Shumakova, “Poor ideal three-edge triangulations are minimal”, Siberian Mathematical Journal, 62:5 (2021), 943–950
6.
A. V. Malyutin, E. A. Fominykh, E. V. Shumakova, “3-manifolds represented by 4-regular graphs with three Eulerian cycles”, Russian Math. Surveys, 76:6 (2021), 1143–1145
2018
7.
P. Cristofori, E. Fominykh, M. Mulazzani, V. Tarkaev, “Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds”, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 112:3 (2018), 781–792
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
9.
V. M. Buchstaber, V. A. Vassiliev, A. Yu. Vesnin, I. A. Dynnikov, Yu. G. Reshetnyak, A. B. Sossinsky, I. A. Taimanov, V. G. Turaev, A. T. Fomenko, E. A. Fominykh, A. V. Chernavsky, “Sergei Vladimirovich Matveev (on his 70th birthday)”, Russian Math. Surveys, 73:4 (2018), 737–746
2017
10.
P. Cristofori, E. Fominykh, M. Mulazzani, V. Tarkaev, “4-colored graphs and knot/link complements”, Results in Mathematics, 72:1-2 (2017), 471–490
2019
11.
E. A. Sbrodova, V. V. Tarkaev, E. A. Fominykh, E. V. Shumakova, “Virtual 3-manifolds of complexity 1 and 2”, Proceedings of the Steklov Institute of Mathematics, 304:Supplement 1 (2019), S154–S160
2017
12.
S. F. Dolbeeva, V. N. Pavlenko, S. V. Matveev, O. N. Dementiev, A. V. Mel'nikov, E. A. Sbrodova, A. A. Soloviev, V. I. Ukhobotov, V. E. Fedorov, E. A. Fominykh, A. A. Ershov, “Arlen Mikhaylovich Il’in. Towards 85th birthday”, Chelyab. Fiz.-Mat. Zh., 2:1 (2017), 5–9
2016
13.
A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Complexity of virtual 3-manifolds”, Sbornik: Mathematics, 207:11 (2016), 1493–1511
14.
E. Fominykh, S. Garoufalidis, M. Goerner, V. Tarkaev, A. Vesnin, “A census of tetrahedral hyperbolic manifolds”, Experimental Mathematics, 25:4 (2016), 466–481
A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Three-dimensional manifolds with poor spines”, Proceedings of the Steklov Institute of Mathematics, 288 (2015), 29–38
2014
16.
A. Yu. Vesnin, E. A. Fominykh, “Two-sided bounds for the complexity of hyperbolic three-manifolds with geodesic boundary”, Proceedings of the Steklov Institute of Mathematics, 286 (2014), 55–64
17.
V. V. Tarkaev, E. A. Fominykh, “Upper bounds for the complexity of some pretzel knots complements”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 6:3 (2014), 50–52
18.
A.Yu. Vesnin, V.V. Tarkaev, E.A. Fominykh, “On the complexity of three-dimensional hyperbolic manifolds with cusps”, Doklady Mathematics, 89:3 (2014), 267–270
2015
19.
A. Yu. Vesnin, V. V. Tarkaev, E. A. Fominykh, “Three-dimensional hyperbolic manifolds with cusps of complexity 10 having maximal volume”, Proceedings of the Steklov Institute of Mathematics, 289, suppl. 1 (2015), 227–239
2013
20.
E. Fominykh, B. Wiest, “Upper bounds for the complexity of torus knot complements”, Journal of Knot Theory and its Ramifications, 22:10 (2013), 1350053 , 19 pp.
A. Yu. Vesnin, E. A. Fominykh, “On complexity of three-dimensional hyperbolic manifolds with geodesic boundary”, Siberian Mathematical Journal, 53:4 (2012), 625–634
2011
22.
E. A. Fominykh, “Dehn surgeries on the figure eight knot: an upper bound for complexity”, Siberian Mathematical Journal, 52:3 (2011), 537–543
E. A. Fominykh, Vestnik Chelyabinsk. Gos. Univ., 2002, no. 6, 25–29
2003
34.
E.A. Fominykh, “A complete description for the set of fundamental surfaces in some 3-manifolds”, translated from Proceedings of the Conference “Geometry and Applications” dedicated to the seventieth birthday of V.A. Toponogov (Novosibirsk, 2000), Siberian Advances in Mathematics, 13, no. 3, 2003, 62–71
2024
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