From manifolds to invariants of E_n-algebras

TL;DR

This thesis introduces a new class of manifold-based invariants for $E_n$-algebras, generalizing topological Hochschild homology, and explores their geometric properties and connections to non-abelian Poincaré duality.

Contribution

It defines these invariants and analyzes their geometric framework, extending previous work by Salvatore and Lurie on topological chiral homology.

Findings

Defined manifold-theoretic invariants for $E_n$-algebras

Connected invariants to non-abelian Poincaré duality

Provided geometric analysis of the invariants

Abstract

This thesis represents the first step in an investigation of an interesting class of manifold-theoretic invariants of $E_n$-algebras which generalize topological Hochschild homology. The main goal of this thesis is to give a definition of the invariants, and analyse their geometric framework. These invariants have appeared in the work of Paolo Salvatore and Jacob Lurie (who calls them topological chiral homology), where they are involved in a sort of non-abelian Poincar\'e duality.