The topology of moment-angle manifolds-on a conjecture of S. Gitler and S. Lopez de Medrano
The topology of moment-angle manifolds-on a conjecture of S. Gitler and S. Lopez de Medrano
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矩角流形的拓扑——基于 S. Gitler 和 S. Lopez de Medrano 的猜想
DOI：
10.1007/s11425-019-1619-7
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Wang Xiangjun
中科院分区：
文献类型：
--
作者：
Chen Liman;Fan Feifei;Wang Xiangjun
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. LetPbe a simple polytope of dimensionnwithmfacets andPvbe a polytope obtained fromPby cutting off one vertexv. LetZ = Z(P) andZv=Z(Pv) be the corresponding moment-angle manifolds. S. Gitler and S. López de Medrano conjectured that:Zvis diffeomorphic to $$\partial \left[ {\left( {Z - {D^{n + m}}} \right) \times {D^2}} \right]\# \,\# _{j = 1}^{m - n}\left( {_j^{m - n}} \right)\left( {{S^{j + 2}} \times {S^{m + n - j - 1}}} \right)$$, and they proved the conjecture in the casem< 3n. In this paper we prove the conjecture in the general case.
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. LetPbe a simple polytope of dimensionnwithmfacets andPvbe a polytope obtained fromPby cutting off one vertexv. LetZ = Z(P) andZv=Z(Pv) be the corresponding moment-angle manifolds. S. Gitler and S. López de Medrano conjectured that:Zvis diffeomorphic to $$\partial \left[ {\left( {Z - {D^{n + m}}} \right) \times {D^2}} \right]\# \,\# _{j = 1}^{m - n}\left( {_j^{m - n}} \right)\left( {{S^{j + 2}} \times {S^{m + n - j - 1}}} \right)$$, and they proved the conjecture in the casem< 3n. In this paper we prove the conjecture in the general case.