The Equivariant Cobordism Category

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.

44 pages; v2 has more details and many improvements; v3 and v4 minor revisions; final accepted version

References in corpus (2)

• Global homotopy theory
• Equivariant iterated loop space theory and permutative G-categories

Cited by in corpus (1)

• Parametrised moduli spaces of surfaces as infinite loop spaces