论文标题
群体复合物的摩尔斯理论
Morse Theory for Complexes of Groups
论文作者
论文摘要
我们构建了一个具有群体动作的简单络合物的离散摩尔斯理论的模棱两可的版本。关键成分是一个2类分类标准，用于在商兼容叠加层组合中的商空间上进行无环的部分匹配。我们使用任何此类兼容匹配的离散流类别类别来构建相应的组组合。我们的主要结果表明，摩尔斯组的发展群体的发展使原始的简单复合物恢复到同型同性恋等效性。
We construct an equivariant version of discrete Morse theory for simplicial complexes endowed with group actions. The key ingredient is a 2-categorical criterion for making acyclic partial matchings on the quotient space compatible with an overlaid complex of groups. We use the discrete flow category of any such compatible matching to build the corresponding Morse complex of groups. Our main result establishes that the development of the Morse complex of groups recovers the original simplicial complex up to equivariant homotopy equivalence.
