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
