PhD Defense Pierre Elis

Title: Equivariant cobordism categories and the homology of moduli spaces of equivariant manifolds

Abstract: 

The goal of this thesis is to study the moduli space MG(M) associated to a smooth compact manifold M equipped with an action of a finite group G. This space is homotopy equivalent to the classifying space of DiffG(M) the topological group of equivariant diffeomorphisms of M. We prove that under some connectivity conditions, its homology is often given by that of an infinite loop space in the stable range, answering a question raised by Galatius-Szucs in [GS21]. We strongly rely on the work of Galatius-Randal-Williams ([GR17a],[GR17b]) on the homology of moduli spaces of high dimensional manifolds, which gave such a stable computation in the non equivariant setting. Our proof relies on the existence of an isotropy separation sequence at the level of equivariant cobordism categories `a la Steimle. As a by-product, we give a new proof of the main result of [GS21]

The thesis for download (pdf)

Advisors:

Søren Galatius, University of Copenhagen, Denmark

Nathalie Wahl, University of Copenhagen, Denmark

Assessment committee: 

Jesper Grodal (chair), University of Copenhagen, Denmark

Irakli Patchkoria, University of Aberdeen, Scotland

Wolfgang Steimle, University of Augsburg, Germany