Periodicity and the values of the real Buchstaber invariants

Abstract

The Buchstaber invariant s(K) is defined to be the maximum integer for which there is a subtorus of dimension s(K) acting freely on the moment-angle complex associated with a finite simplicial complex K. Analogously, its real version s(R)(K) can also be defined by using the real moment angle complex instead of the moment-angle complex. The importance of these invariants comes from the fact that s(K) and s(R)(K) distinguish two simplicial complexes and are the source of nontrivial and interesting combinatorial tasks. The ultimate goal of this paper is to compute the real Buchstaber invariants of skeleta K = Delta(m-1)(m-p-1) of the simplex Delta(m-1) by making a formula. In fact, it can be solved by integer linear programming. We also give a counterexample to the conjecture which is proposed in [6] and we provide an adjusted formula which can be thought of as a preperiodicity of some numbers related to the real Buchstaber invariants