25 citations · 171 across the 21 of their papers we have counts for
4 papers · 1 filter
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…
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…
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…