Toric manifolds and colorings of discrete structures

Abstract

Small covers and quasitoric manifolds are topological generalizations of smooth projective toric varieties. Their topological features are determined by combinatorial polytopes that are the orbit space of the corresponding actions of a real and a complex torus. Therefore, many important problems in toric topology can be reduced to problems of generalized colourings of discrete structures such as graphs and simplicial complexes. This talk presents some of them and explains deep correlations among combinatorics, algebra and topology.