PhD Defense Branko Juran

Titel: Equivariant homotopy theory and higher category theory

Abstract:

This thesis is divided into two parts. In the first part, we prove an equivariant generalization of the recognition principle: We show that for G a finite group and V a G-representation, an EV -algebra in G-spaces is equivalent to a V -fold loop space if and only if it is group-like. In the second part of this thesis, we show that the category of orthogonal factorization systems embeds fully faithfully into the category of double categories, a result which is used to construct an equivariant symmetric monoidal structure on the category of equivariant manifolds.

Thesis 

Advisor: Professor Jesper Grodal, University of Copenhagen

Assessment Committee:

Chair, Professor Nathalie Wahl. University of Copenhagen 

Associate Professor, Emanuelle Dotto, Warwick University

Lecturer, Irakli Patchkoria, University of Aberdeen