发表机构
Moscow State University; Steklov Mathematical Institute of Russian Academy of Sciences; National Research University Higher School of Economics; Institute for Information Transmission Problems, Russian Academy of Sciences（莫斯科国立大学; 俄罗斯科学院斯捷克洛夫数学研究所; 国立高等经济大学; 俄罗斯科学院信息传输问题研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明两类星形单纯球面（三维带两条不相邻缺失边及奇数维邻接型）对应的矩角流形微分同胚于球面乘积的连通和，并显式描述非多面体Barnette与Brückner球面的情形。
AI 中文摘要
我们证明，当$\mathcal K$是一个星形（特别是多面体）的三维单纯球面，且恰好有两条不相邻的缺失边时，矩角流形$\mathcal Z_{\mathcal K}$与球面乘积的连通和微分同胚。该连通和的一个被加项是三个球面的乘积。对于奇数维的邻接星形单纯球面$\mathcal K$，我们证明微分同胚$\mathcal Z_{\mathcal K} \cong M_1\\#\cdots\\# M_k$，其中每个$M_i$是两个球面的乘积。我们给出了对应于非多面体的Barnette球面和Brückner球面的矩角流形的显式描述。
英文摘要
We prove that the moment-angle manifold $\mathcal Z_{\mathcal K}$ is diffeomorphic to a connected sum of products of spheres when $\mathcal K$ is a starshaped (in particular, polytopal) 3-dimensional simplicial sphere with exactly two missing edges that are not adjacent to each other. One of the summands of the connected sum is a product of three spheres. For neighbourly starshaped simplicial spheres $\mathcal K$ of odd dimension, we prove the diffeomorphism $\mathcal Z_{\mathcal K} \cong M_1\#\cdots\# M_k$, where each $M_i$ is a product of two spheres. We give an explicit description of the moment-angle manifolds corresponding to non-polytopal Barnette and Brückner spheres.
Comments23 pages, LaTeX
