# Factorization homology of stratified spaces

@article{Ayala2014FactorizationHO, title={Factorization homology of stratified spaces}, author={David Ayala and John Francis and Hiro Tanaka}, journal={Selecta Mathematica}, year={2014}, volume={23}, pages={293-362} }

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…

## 66 Citations

Factorization homology of topological manifolds

- Mathematics
- 2012

Factorization homology theories of topological manifolds, after Beilinson, Drinfeld, and Lurie, are homology‐type theories for topological n ‐manifolds whose coefficient systems are n ‐disk algebras…

Betti numbers and stability for configuration spaces via factorization homology

- Mathematics
- 2017

Using factorization homology, we realize the rational homology of the unordered configuration spaces of an arbitrary manifold $M$, possibly with boundary, as the homology of a Lie algebra constructed…

Higher enveloping algebras

- MathematicsGeometry & Topology
- 2018

We provide spectral Lie algebras with enveloping algebras over the operad of little $G$-framed $n$-dimensional disks for any choice of dimension $n$ and structure group $G$, and we describe these…

Topological orders and factorization homology

- Mathematics
- 2016

In the study of 2d (the space dimension) topological orders, it is well-known that bulk excitations are classified by unitary modular tensor categories. But these categories only describe the local…

A Simplicial Approach to Stratified Homotopy Theory

- Mathematics
- 2019

This thesis provides a framework to study the homotopy theory of stratified spaces, in a way that is compatible with previous approaches. In particular our approach will be closely related to the…

Secondary Products in Supersymmetric Field Theory

- Mathematics
- 2018

The product of local operators in a topological quantum field theory in dimension greater than one is commutative, as is more generally the product of extended operators of codimension greater than…

Finite symmetries of quantum character stacks

- Mathematics
- 2021

For a finite group D, we study categorical factorisation homology on oriented surfaces equipped with principal D-bundles, which ‘integrates’ a (linear) balanced braided category A with D-action over…

Equivariant localization in factorization homology and applications in mathematical physics II: Gauge theory applications

- Mathematics
- 2020

We give an account of the theory of factorization spaces, categories, functors, and algebras, following the approach of [Ras1]. We apply these results to give geometric constructions of factorization…

On the combinatorics of exact Lagrangian surfaces

- Mathematics
- 2016

We study Weinstein 4-manifolds which admit Lagrangian skeleta given by attaching disks to a surface along a collection of simple closed curves. In terms of the curves describing one such skeleton, we…

Explorer Integrating quantum groups over surfaces

- Mathematics
- 2018

We apply the mechanism of factorization homology to construct and compute category-valued two-dimensional topological field theories associated to braided tensor categories, generalizing the (0, 1,…

## References

SHOWING 1-10 OF 38 REFERENCES

Factorization homology of topological manifolds

- Mathematics
- 2012

Factorization homology theories of topological manifolds, after Beilinson, Drinfeld, and Lurie, are homology‐type theories for topological n ‐manifolds whose coefficient systems are n ‐disk algebras…

Chiral Koszul duality

- Mathematics
- 2011

We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American Mathematical Society,…

Higher dimensional algebra and topological quantum field theory

- Mathematics
- 1995

The study of topological quantum field theories increasingly relies upon concepts from higher‐dimensional algebra such as n‐categories and n‐vector spaces. We review progress towards a definition of…

Intersection homology II

- Mathematics
- 1983

In [19, 20] we introduced topological invariants IH~,(X) called intersection homology groups for the study of singular spaces X. These groups depend on the choice of a perversity p: a perversity is a…

A stratified homotopy hypothesis

- MathematicsJournal of the European Mathematical Society
- 2018

We show that conically smooth stratified spaces embed fully faithfully into $\infty$-categories. This articulates a stratified generalization of the homotopy hypothesis proposed by Grothendieck. As…

Configuration-spaces and iterated loop-spaces

- Mathematics
- 1973

The object of this paper is to prove a theorem relating "configurationspaces" to iterated loop-spaces. The idea of the connection between them seems to be due to Boardman and Vogt [2]. Part of the…

The geometry of iterated loop spaces

- Mathematics
- 1972

Operads and -spaces.- Operads and monads.- A? and E? operads.- The little cubes operads .- Iterated loop spaces and the .- The approximation theorem.- Cofibrations and quasi-fibrations.- The smash…

A comprehensive introduction to differential geometry

- Mathematics
- 1975

Spivak's Comprehensive introduction takes as its theme the classical roots of contemporary differential geometry. Spivak explains his Main Premise (my term) as follows: "in order for an introduction…