The topology of the moment-angle manifolds--On a conjecture of S. Gitler ans S. Lopez

Abstract

Let $P$ be a simple polytope of dimension $n$ with $m$ facets and $P_v$ be a polytope obtained from $P$ by cutting off one vertex $v$. Let $Z=Z(P)$ and $Z_v=Z(P_v)$ be the corresponding moment-angle manifolds. In \cite{[GL]} S.Gitler and S.López conjectured that: $Z_v$ is diffeomorphic to $\partial [(Z-int(D^{n+m}))\times D^2]♯\underset{j=1}{\overset{m-n}{♯}}\left(\genfrac{}{}{0ex}{}{m-n}{j}\right)(S^{j+2}\times S^{m+n-j-1})$, and they have proved the conjecture in the case $m<3n$. In this paper we prove the conjecture in general case.

arXiv comment11 pages, 2 figures

Cited by in corpus (2)

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• Simplicial $G$-complexes and representation stability of polyhedral products