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, D. A. Gorodkov, “An explicit local combinatorial formula for the first Pontryagin class”, Russian Math. Surveys, 74:6 (2019), 1120–1122
2018
2.
Alexander A. Gaifullin, Leonid S. Ignashchenko, “Dehn invariant and scissors congruence of flexible polyhedra”, Proc. Steklov Inst. Math., 302 (2018), 130–145 (cited: 3) (cited: 3)
3.
Alexander A. Gaifullin, Yury A. Neretin, “Infinite symmetric group, pseudomanifolds, and combinatorial cobordism-like structures”, J. Topol. Anal., 10:3 (2018), 605–625 (cited: 1)
2017
4.
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 (cited: 2) (cited: 3) (cited: 3)
5.
A. A. Gaifullin, “On an extension of the Birman–Craggs–Johnson homomorphism”, Russian Math. Surveys, 72:6 (2017), 1171–1173
2016
6.
A. A. Gaifullin, Flexible Polyhedra and Their Volumes, 2016 , 20 pp., arXiv: 1605.09316
7.
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
8.
A. A. Gaifullin, “Small covers of graph-associahedra and realization of cycles”, Sb. Math., 207:11 (2016), 1537–1561 (cited: 2) (cited: 2)
2015
9.
A. A. Gaifullin, Yu. A. Neretin, Infinite symmetric group and bordisms of pseudomanifolds, 2015 , 14 pp., arXiv: 1501.04062
10.
A. A. Gaifullin, “Embedded flexible spherical cross-polytopes with nonconstant volumes”, Proc. Steklov Inst. Math., 288 (2015), 56–80 , arXiv: 1501.06198 (cited: 5) (cited: 1) (cited: 1) (cited: 4)
11.
A. A. Gaifullin, “The analytic continuation of volume and the Bellows conjecture in Lobachevsky spaces”, Sb. Math., 206:11 (2015), 1564–1609 (cited: 6) (cited: 5)
2014
12.
A. A. Gaifullin, “Sabitov polynomials for volumes of polyhedra in four dimensions”, Adv. Math., 252 (2014), 586–611 , arXiv: 1108.6014 (cited: 11) (cited: 7) (cited: 12)
13.
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
14.
A. A. Gaifullin, “Flexible cross-polytopes in spaces of constant curvature”, Proc. Steklov Inst. Math., 286 (2014), 77–113 , arXiv: 1312.7608 (cited: 11) (cited: 3) (cited: 3) (cited: 7)
15.
A. A. Gaifullin, “Generalization of Sabitov's theorem to polyhedra of arbitrary dimensions”, Discrete Comput. Geom., 52:2 (2014), 195–220 , arXiv: 1210.5408 (cited: 11) (cited: 4)
16.
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
17.
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
2013
20.
A. A. Gaifullin, “Universal realisators for homology classes”, Geometry & Topology, 17:3 (2013), 1745–1772 http://www.msp.warwick.ac.uk/gt/2013/17-03/p039.xhtml, arXiv: 1201.4823 (cited: 11) (cited: 7) (cited: 11)
21.
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
22.
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
23.
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
2012
24.
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
25.
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
26.
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
27.
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
28.
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
29.
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 (cited: 2) (cited: 2)
30.
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
31.
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
32.
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
33.
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
34.
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 (cited: 4) (cited: 2)
35.
A. A. Gaifullin, “Realisation of cycles by aspherical manifolds”, Russian Math. Surveys, 63:3 (2008), 562–564 , arXiv: 0806.3580 (cited: 5) (cited: 2)
36.
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 (cited: 5) (cited: 1) (cited: 1) (cited: 3)
37.
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
38.
A. A. Gaifullin, Kombinatornaya realizatsiya tsiklov, Diss. … kand. fiz.-matem. nauk, MGU im. M.V. Lomonosova, Mekhaniko-matematicheskii fakultet, Moskva, 2008 , 121 pp.
2007
39.
A. A. Gaifullin, “Explicit construction of manifolds realising prescribed homology classes”, Russian Math. Surveys, 62:6 (2007), 1199–1201 , arXiv: 0712.1709 (cited: 4) (cited: 1) (cited: 1) (cited: 1)
40.
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 (cited: 1) (cited: 1) (cited: 1)
2006
41.
V. M. Buchstaber, A. A. Gaifullin, “Representations of $m$-valued groups on triangulations of manifolds”, Russian Math. Surveys, 61:3 (2006), 560–562 (cited: 2) (cited: 2) (cited: 2) (cited: 3)
2005
42.
A. A. Gaifullin, “Computation of characteristic classes of a manifold from a triangulation of it”, Russian Math. Surveys, 60:4 (2005), 615–644 (cited: 3) (cited: 4) (cited: 4) (cited: 1)
2004
43.
A. A. Gaifullin, “Local formulae for combinatorial Pontryagin classes”, Izv. Math., 68:5 (2004), 861–910 , arXiv: math/0407035 (cited: 8) (cited: 2) (cited: 4)
44.
A. A. Gaifullin, “On local formulae for combinatorial Pontryagin classes of manifolds”, Russian Math. Surveys, 59:2 (2004), 379–380
2003
45.
A. A. Gaifullin, “Nerves of Coxeter groups”, Russian Math. Surveys, 58:3 (2003), 615–616
A. A. Gaifullin, V. O. Manturov, “On the recognition of braids”, J. Knot Theory Ramifications, 11:8 (2002), 1193–1209 (cited: 1) (cited: 1) (cited: 3)
2001
48.
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
Presentations in Math-Net.Ru
1.
О гомологиях групп Торелли A. A. Gaifullin Meetings of the Moscow Mathematical Society December 8, 2020 19:20
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 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 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 January 19, 2011 14:00
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, Tr. 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