Factorization homology of stratified spaces

Understand

This work forms a foundational study of factorization homology, or topological chiral homology, at the generality of stratified spaces with tangential structures.

• Examples of such factorization homology theories include intersection homology, compactly supported stratified mapping spaces, and Hochschild homology with coefficients.
• Our main theorem characterizes factorization homology theories by a generalization of the Eilenberg--Steenrod axioms; it can also be viewed as an analogue of the Baez--Dolan cobordism hypothesis formulated for the observables, rather than state spaces, of a topological quantum field theory.
• Using these axioms, we extend the nonabelian Poincar\'e duality of Salvatore and Lurie to the setting of stratified spaces -- this is a nonabelian version of the Poincar\'e duality given by intersection homology.