论文标题
莫尔斯复合物的较高连通性
Higher connectivity of the Morse complex
论文作者
论文摘要
有限的简单复合物$δ$的Morse Complex $ \ Mathcal {M}（δ）$是$δ$上所有梯度矢量字段的复合体。在本文中，我们研究了$ \ Mathcal {M}（δ）$的较高连接性能。例如，我们证明$ \ Mathcal {m}（δ）$随着$Δ$的最大值为$ \ infty $，随着$ \ undty $的最大程度连接，并且每图$δ$，因为边缘数量为$ \ infty $。当连接或简单连接时，我们还精确地对$ \ Mathcal {M}（M}（δ）$进行分类。我们的主要工具是Bestvina-Brady Morse理论，应用于“广义摩尔斯复合体”。
The Morse complex $\mathcal{M}(Δ)$ of a finite simplicial complex $Δ$ is the complex of all gradient vector fields on $Δ$. In this paper we study higher connectivity properties of $\mathcal{M}(Δ)$. For example, we prove that $\mathcal{M}(Δ)$ gets arbitrarily highly connected as the maximum degree of a vertex of $Δ$ goes to $\infty$, and for $Δ$ a graph additionally as the number of edges goes to $\infty$. We also classify precisely when $\mathcal{M}(Δ)$ is connected or simply connected. Our main tool is Bestvina-Brady Morse theory, applied to a "generalized Morse complex."
