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, “Commutativity of involutive two-valued groups”, Russian Math. Surveys, 79:2 (2024), 363–365 , arXiv: 2401.15191
3.
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
4.
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
5.
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 , 397 pp.
2023
6.
A. A. Gaifullin, “On infinitely generated homology of Torelli groups”, Algebra i analiz, 35:6 (2023), 87–134 , arXiv: 1803.09311;
2022
7.
Alexander A. Gaifullin, “On the top homology group of the Johnson kernel”, Mosc. Math. J., 22:1 (2022), 83–102 , arXiv: 1903.03864;
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
9.
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.
10.
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.
2021
11.
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
2019
12.
A. A. Gaifullin, D. A. Gorodkov, “An explicit local combinatorial formula for the first Pontryagin class”, Russian Math. Surveys, 74:6 (2019), 1120–1122
13.
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.
14.
N. Agakhanov, D. Belov, I. Bogdanov, A. Gaifullin, M. Grigor'ev, P. Kozhevnikov, O. Podlipsky, Kvant, 2019, no. 7, 40–43
15.
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
2018
16.
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
17.
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
N. H. Agakhanov, I. I. Bogdanov, A. A. Gaifullin, P. A. Kozhevnikov, Kvant, 2018, no. 8, 39–41
2017
19.
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
A. A. Gaifullin, “On an extension of the Birman–Craggs–Johnson homomorphism”, Russian Math. Surveys, 72:6 (2017), 1171–1173
2016
21.
A. A. Gaifullin, Flexible Polyhedra and Their Volumes, 2016 , 20 pp., arXiv: 1605.09316
22.
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
23.
A. A. Gaifullin, “Small covers of graph-associahedra and realization of cycles”, Sb. Math., 207:11 (2016), 1537–1561 , arXiv: 1611.01816
2015
24.
A. A. Gaifullin, “Embedded flexible spherical cross-polytopes with nonconstant volumes”, Proc. Steklov Inst. Math., 288 (2015), 56–80 , arXiv: 1501.06198
25.
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
26.
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
2014
27.
A. A. Gaifullin, “Sabitov polynomials for volumes of polyhedra in four dimensions”, Adv. Math., 252 (2014), 586–611 , arXiv: 1108.6014
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, “Flexible cross-polytopes in spaces of constant curvature”, Proc. Steklov Inst. Math., 286 (2014), 77–113 , arXiv: 1312.7608
30.
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, “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
32.
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
35.
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
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
38.
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
39.
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. 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
41.
A. A. Gaifullin, T. E. Panov, “Victor Matveevich Buchstaber’s 70th birthday anniversary”, Trans. Moscow Math. Soc., 2013 (2013), 173
2012
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
2011
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
2010
47.
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
48.
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
49.
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
50.
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.
2009
51.
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
2008
52.
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
53.
A. A. Gaifullin, “Realisation of cycles by aspherical manifolds”, Russian Math. Surveys, 63:3 (2008), 562–564 , arXiv: 0806.3580
54.
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
55.
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
56.
A. A. Gaifullin, Kombinatornaya realizatsiya tsiklov, Diss. … kand. fiz.-matem. nauk, MGU im. M.V. Lomonosova, Mekhaniko-matematicheskii fakultet, Moskva, 2008 , 121 pp.
2007
57.
A. A. Gaifullin, “Explicit construction of manifolds realising prescribed homology classes”, Russian Math. Surveys, 62:6 (2007), 1199–1201 , arXiv: 0712.1709
58.
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
2006
59.
V. M. Buchstaber, A. A. Gaifullin, “Representations of $m$-valued groups on triangulations of manifolds”, Russian Math. Surveys, 61:3 (2006), 560–562
2005
60.
A. A. Gaifullin, “Computation of characteristic classes of a manifold from a triangulation of it”, Russian Math. Surveys, 60:4 (2005), 615–644
2004
61.
A. A. Gaifullin, “Local formulae for combinatorial Pontryagin classes”, Izv. Math., 68:5 (2004), 861–910 , arXiv: math/0407035
62.
A. A. Gaifullin, “On local formulae for combinatorial Pontryagin classes of manifolds”, Russian Math. Surveys, 59:2 (2004), 379–380
2003
63.
A. A. Gaifullin, “Nerves of Coxeter groups”, Russian Math. Surveys, 58:3 (2003), 615–616
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
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, 397 с. 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