The formula for the real Buchstaber invariants of skeleta of a simplex
[The 4th Korea Toric Topology Winter Workshop]
Hyun Woong Cho (KIAS)
The Buchstaber invariants s(K) is deﬁned to be the maximum integer for which there is a subtorus of dimension s(K) acting freely on moment angle complex Z_K associated with a ﬁnite simplicial complex K. We can deﬁne real Buchstaber invariants sR(K) as a real version. When K is a (m−p−1) skeleton of (m−1) dimensional simplex, say K = ∆m-1m-p-1 , we can ﬁnd the values of sR(K) by solving integer linear programming. In this case, the condition for sR(K) ≥ k is given by some nice formula. However, this formula holds when a certain condition is satisﬁed. This condition come from the dual problem of integer linear programming. Additionally, I will talk about the (pre)periodicity of the real Buchstaber invariants in some sense.
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