The equivariant cobordism category

摘要

For a finite group G, we define an equivariant cobordism category CdG. 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.