25 citations · 171 across the 21 of their papers we have counts for
21 papers
On possible symmetry groups of 27-vertex triangulations of manifolds like the octonionic projective plane
Alexander A. Gaifullin
In 1987 Brehm and Kühnel showed that any triangulation of a -manifold (without boundary) that is not homeomorphic to the sphere has at least vertices. Moreover, triangu…
Classification of involutive commutative two-valued groups
Victor M. Buchstaber, Alexander A. Gaifullin, Alexander P. Veselov
A complete classification of finitely generated involutive commutative two-valued groups is obtained. Three series of such two-valued groups are constructed: principal, unipotent a…
On spectral sequence for the action of genus 3 Torelli group on the complex of cycles
Alexander A. Gaifullin
The Torelli group of a genus oriented surface is the subgroup of the mapping class group consisting of all mapping classes that act tr…
On the top homology group of Johnson kernel
Alexander A. Gaifullin
The action of the mapping class group of an oriented surface on the lower central series of defines the descending filtration in …
On infinitely generated homology of Torelli groups
Alexander A. Gaifullin
Let be the Torelli group of an oriented closed surface of genus , that is, the kernel of the action of the mapping class group on the first integral homolo…
Dehn invariant of flexible polyhedra
Alexander A. Gaifullin, Leonid Ignashchenko
We prove that the Dehn invariant of any flexible polyhedron in Euclidean space of dimension greater than or equal to 3 is constant during the flexion. In dimensions 3 and 4 this im…
Flexible Polyhedra and Their Volumes
Alexander A. Gaifullin
We discuss some recent results on flexible polyhedra and the bellows conjecture, which claims that the volume of any flexible polyhedron is constant during the flexion. Also, we su…
The bellows conjecture for small flexible polyhedra in non-Euclidean spaces
Alexander A. Gaifullin
The bellows conjecture claims that the volume of any flexible polyhedron of dimension 3 or higher is constant during the flexion. The bellows conjecture was proved for flexible pol…
Embedded flexible spherical cross-polytopes with non-constant volumes
Alexander A. Gaifullin
We construct examples of embedded flexible cross-polytopes in the spheres of all dimensions. These examples are interesting from two points of view. First, in dimensions 4 and high…
Infinite symmetric group and bordisms of pseudomanifolds
Alexander A. Gaifullin, Yury A. Neretin
We consider a category whose morphisms are bordisms of -dimensional pseudomanifolds equipped with a certain additional structure (coloring). On the other hand, we consider the p…
Flexible cross-polytopes in spaces of constant curvature
Alexander A. Gaifullin
We construct self-intersected flexible cross-polytopes in the spaces of constant curvature, that is, the Euclidean spaces, the spheres, and the Lobachevsky spaces of all dimensions…
Volume of a simplex as a multivalued algebraic function of the areas of its two-faces
Alexander A. Gaifullin
For n greater than or equal to 4, the square of the volume of an n-simplex satisfies a polynomial relation with coefficients depending on the squares of the areas of 2-faces of thi…
Deformations of period lattices of flexible polyhedral surfaces
Alexander A. Gaifullin, Sergey A. Gaifullin
In the end of the 19th century Bricard discovered a phenomenon of flexible polyhedra, that is, polyhedra with rigid faces and hinges at edges that admit non-trivial flexes. One of…
Generalization of Sabitov's Theorem to Polyhedra of Arbitrary Dimensions
Alexander A. Gaifullin
In 1996 Sabitov proved that the volume of an arbitrary simplicial polyhedron P in the 3-dimensional Euclidean space satisfies a monic (with respect to V) polynomial relation…
Combinatorial realisation of cycles and small covers
Alexander A. Gaifullin
In 1940s Steenrod asked if every homology class of every topological space can be realised by an image of the fundamental class of an oriented closed s…
Universal Realisators for Homology Classes
Alexander A. Gaifullin
We study oriented closed manifolds M^n possessing the following Universal Realisation of Cycles (URC) Property: For each topological space X and each integral homology class z of i…
Sabitov polynomials for volumes of polyhedra in four dimensions
Alexander A. Gaifullin
In 1996 I.Kh. Sabitov proved that the volume of a simplicial polyhedron in a 3-dimensional Euclidean space is a root of certain polynomial with coefficients depending on the combin…
Configuration spaces, bistellar moves, and combinatorial formulae for the first Pontryagin class
Alexander A. Gaifullin
The paper is devoted to the problem of finding explicit combinatorial formulae for the Pontryagin classes. We discuss two formulae, the classical Gabrielov-Gelfand-Losik formula ba…
A minimal triangulation of complex projective plane admitting a chess colouring of four-dimensional simplices
Alexander A. Gaifullin
In this paper we construct and study a new 15-vertex triangulation of the complex projective plane $\CP^2$. The automorphism group of is isomorphic to . We p…
Realisation of cycles by aspherical manifolds
Alexander A. Gaifullin
We develop a new purely combinatorial approach to N. Steenrod's problem on realisation of cycles. We prove that every n-dimensional homology class of every topological space can be…
Explicit construction of manifolds realizing the prescribed homology classes
A. A. Gaifullin
We consider a classical N. Steenrod's problem on realization of homology classes by images of the fundamental classes of manifolds. It is well-known that each integral homology cla…