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The equivariant cobordism category
Journal of Topology ( IF 1.1 ) Pub Date : 2021-01-07 , DOI: 10.1112/topo.12181
Søren Galatius 1 , Gergely Szűcs
Affiliation  

For a finite group G , we define an equivariant cobordism category C d G . Objects of the category are ( d 1 ) ‐dimensional closed smooth G ‐manifolds and morphisms are smooth d ‐dimensional equivariant cobordisms. We identify the homotopy type of its classifying space (that is, geometric realization of its simplicial nerve) as the fixed points of the infinite loop space of a certain equivariant Thom spectrum.

中文翻译:

等变共生主义类别

对于一个有限的群体 G ,我们定义了等变的cobordism类别 C d G 。类别的对象是 d - 1个 尺寸封闭平滑 G 流形和态射是平滑的 d 维等变cobordisms。我们将其分类空间的同伦类型(即其简单神经的几何实现)识别为某个等变Thom谱的无限环空间的不动点。
更新日期:2021-01-07
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