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 $s_{\mathbb{R}}(K)$ 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 $s_{\mathbb{R}}(K)$ 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 $K=\Delta_{m-p-1}^{m-1}$ 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.
Citation
Hyun Woong CHO. "Periodicity and the values of the real Buchstaber invariants." J. Math. Soc. Japan 68 (4) 1695 - 1723, October, 2016. https://doi.org/10.2969/jmsj/06841695
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