Structured singular manifolds and factorization homology

Understand

We provide a framework for the study of structured manifolds with singularities and their locally determined invariants.

• This generalizes factorization homology, or topological chiral homology, to the setting of singular manifolds equipped with various tangential structures.
• Examples of such factorization homology theories include intersection homology, compactly supported stratified mapping spaces, and Hochschild homology with coefficients.
• Factorization homology theories for singular manifolds are characterized by a generalization of the Eilenberg-Steenrod axioms.