The topology of moment-angle manifolds—on a conjecture of S. Gitler and S. López de Medrano

In this paper, we study the topology of moment-angle manifolds and prove a conjecture of S. Gitler and S. López de Medrano concerned with the behavior of the moment-angle manifold under the surgery ‘cutting off a vertex’ on a simple polytope. Let P be a simple polytope of dimension n with m facets a...

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Bibliographic Details
Published in:Science China. Mathematics 2020-10, Vol.63 (10), p.2079-2088
Main Authors: Chen, Liman, Fan, Feifei, Wang, Xiangjun
Format: Article
Language:English
Subjects:
Applications of Mathematics
Cutting parameters
Manifolds (mathematics)
Mathematics
Mathematics and Statistics
Topology
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Summary:In this paper, we study the topology of moment-angle manifolds and prove a conjecture of S. Gitler and S. López de Medrano concerned with the behavior of the moment-angle manifold under the surgery ‘cutting off a vertex’ on a simple polytope. 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. S. Gitler and S. López de Medrano conjectured that: Z v is diffeomorphic to , and they proved the conjecture in the case m < 3 n . In this paper we prove the conjecture in the general case.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-019-1619-7