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June 2011 Buchstaber invariants of skeleta of a simplex
Yukiko Fukukawa, Mikiya Masuda
Osaka J. Math. 48(2): 549-582 (June 2011).

Abstract

A moment-angle complex ZK is a compact topological space associated with a finite simplicial complex K. It is realized as a subspace of a polydisk (D2)m, where m is the number of vertices in K and D2 is the unit disk of the complex numbers C, and the natural action of a torus (S1)m on (D2)m leaves ZK invariant. The Buchstaber invariant s(K) of K is the largest integer for which there is a subtorus of rank s(K) acting on ZK freely. The story above goes over the real numbers R in place of C and a real analogue of the Buchstaber invariant, denoted sR(K), can be defined for K and s(K)sR(K). In this paper we will make some computations of sR(K) when K is a skeleton of a simplex. We take two approaches to find sR(K) and the latter one turns out to be a problem of integer linear programming and of independent interest.

Citation

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Yukiko Fukukawa. Mikiya Masuda. "Buchstaber invariants of skeleta of a simplex." Osaka J. Math. 48 (2) 549 - 582, June 2011.

Information

Published: June 2011
First available in Project Euclid: 6 September 2011

zbMATH: 1238.57031
MathSciNet: MR2831986

Subjects:
Primary: 57S17
Secondary: 90C10

Rights: Copyright © 2011 Osaka University and Osaka City University, Departments of Mathematics

Vol.48 • No. 2 • June 2011
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