Homology and manifolds with corners

TL;DR

This paper introduces a new homology model for manifolds with corners, enabling the definition of intersection products and homological quantum field theories, extending string topology and homotopy quantum field theories.

Contribution

It develops a homology framework for manifolds with corners and generalizes string topology and quantum field theories within this context.

Findings

Defined a homology model for manifolds with corners

Described intersection products on homology of compact oriented manifolds

Introduced homological quantum field theories

Abstract

We define a model for the homology of manifolds and use it to describe the intersection product on the homology of compact oriented manifolds and to define homological quantum field theories which generalizes the notions of string topology introduced by Chas and Sullivan and homotopy quantum field theories introduced by Turaev.