Mod p Buchstaber invariant

Abstract

In this talk, we present combinatorial and topological properties of the universal complexes X(Fn p ) and K(Fn p ) whose simplices are certain unimod- ular subsets of Fn p . We calculate their f -vectors and the bigraded Betti numbers of their Tor-algebras, show that they are shellable, and find their applications in toric topology and number theory. We showed that the Lusternick-Schnirelmann category of the moment angle complex of X(Fn p ) is n, provided p is an odd prime and the Lusternick-Schnirelmann category of the moment angle complex of K(Fn p ) is [ n 2 ]. Based on the universal com- plexes, we introduce the Buchstaber invariant sp for a prime number p. We investigate the mod p Buchstaber invariant of the skeleta of simplices for a prime number p and compare them for different values of p. For p = 2, the invariant is the real Buchstaber invariant. Our findings reveal that these val- ues are generally distinct. Additionally, we determine or estimate the mod p Buchstaber invariants of some universal simplicial complexes X(Fn p ). The talk is based on joint research with Aleˇs Vavpeti´c and Aleksandar Vuˇci´c.