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arXiv · 1805.12342

The Equivariant Cobordism Category

Gergely Szűcs·Søren Galatius
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Abstract

For a finite group $G$, we define an equivariant cobordism category $\mathcal{C}_d^G$. 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 (i.e. geometric realization of its simplicial nerve) as the fixed points of the infinite loop space of an equivariant spectrum.

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BibTeXRIS

Gergely Szűcs, Søren Galatius. 2020-11-27. The Equivariant Cobordism Category. https://doi.org/10.1112/topo.12181

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