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
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, E. A. Fominykh, “On complexity of three-dimensional hyperbolic manifolds with geodesic boundary”, Siberian Mathematical Journal, 53:4 (2012), 625–634
3.
A.Yu. Vesnin, E.A. Fominykh, “Exact values of complexity for Paoluzzi-Zimmermann manifolds”, Doklady Mathematics, 84:1 (2011), 542–544
4.
E. A. Fominykh, “Dehn surgeries on the figure eight knot: an upper bound for complexity”, Siberian Mathematical Journal, 52:3 (2011), 537–543
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, V.V. Tarkaev, E.A. Fominykh, “On the complexity of three-dimensional hyperbolic manifolds with cusps”, Doklady Mathematics, 89:3 (2014), 267–270
8.
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
9.
A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Complexity of virtual 3-manifolds”, Sbornik: Mathematics, 207:11 (2016), 1493–1511
10.
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
11.
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
12.
E. A. Fominykh, M. A. Ovchinnikov, “On the complexity of graph-manifolds”, Sibirskie elektronnye matematicheskie izvestiya, 2 (2005), 190–191
E. A. Fominykh, “Upper complexity bounds for an infinite family of graph-manifolds”, Sib. Èlektron. Mat. Izv., 5 (2008), 215–228
16.
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
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
18.
E. A. Fominykh, E. V. Shumakova, “Poor ideal three-edge triangulations are minimal”, Siberian Mathematical Journal, 62:5 (2021), 943–950
19.
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
20.
P. Cristofori, E. Fominykh, M. Mulazzani, V. Tarkaev, “4-colored graphs and knot/link complements”, Results in Mathematics, 72:1-2 (2017), 471–490
21.
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
22.
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
23.
E.A. Fominykh, “Verkhnie otsenki slozhnosti mnogoobrazii, skleennykh iz dvukh mnogoobrazii Zeiferta s bazoi disk i dvumya osobymi sloyami”, Vestnik Kemerovskogo gosudarstvennogo universiteta, 3/1 (2011), 83–88
24.
E.A. Fominykh, “3-manifolds of low complexity that possess the geometries $S^3$ and $Nil$”, Vestn. Chelyab. Gos. Univ. Mat. Mekh. Inform, 2010, no. 23 (12), 98–103
25.
E. A. Fominykh, “A complete description of normal surfaces for infinite series of 3-manifolds”, Siberian Mathematical Journal, 43:6 (2002), 1112–1123
E. A. Fominykh, Vestnik Chelyabinsk. Gos. Univ., 2002, no. 6, 25–29
29.
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
30.
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
31.
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
32.
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