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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
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 , we define an equivariant cobordism category . Objects of the category are ‐dimensional closed smooth ‐manifolds and morphisms are smooth ‐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 ,我们定义了等变的cobordism类别 。类别的对象是尺寸封闭平滑 流形和态射是平滑的 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
中文翻译:
等变共生主义类别
对于一个有限的群体 ,我们定义了等变的cobordism类别 。类别的对象是尺寸封闭平滑 流形和态射是平滑的 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。