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The equivariant cobordism category
Journal of Topology  (IF1.582),  Pub Date : 2021-01-07, DOI: 10.1112/topo.12181
Søren Galatius, Gergely Szűcs

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.