PhD Defense Espen Auseth Nielsen

Abstract:

This thesis is a contribution to the recently popular field of operations on Hochschild (co-)homology of rings. This field has connections to the geometry of free loop spaces of manifolds and to topological quantum field theories.

The thesis consists of three papers. The first paper discusses operations on the Hochschild homology of structured algebras, all of whose structure morphisms are algebraic. In particular we obtain a strict model for the coherent commutative Hopf algebra structure on the Hochschild homology of commutative Hops algebras.

The second paper discusses the coherent commutative Hops algebra structure on more general commutative Hopf-like algebras, such as quasi-Hopf algebras and Hopfish algebras.

The third paper is a work in progress discussing operations on topological Hochschild homology and applications to open-closed conformal field theory.

Supervisor:.Prof. Nathalie Wahl, MATH, University of Copenhagen

Assessment Committee:

Prof. (Chairman), Søren Galatius, Math, University of Copenhagen

Prof. Birgit Richter, University of Hamburg

Prof. Marcel Bokstedt, University of Aarhus