Factorization homology of stratified spaces
详细信息 查看全文
- 作者：David Ayala ; John Francis ; Hiro Lee Tanaka
- 关键词：Factorization homology ; Topological quantum field theory ; Topological chiral homology ; Knot homology ; Configuration spaces ; Operads ; \({{\mathrm{\infty }}}\) ; Categories
- 刊名：Selecta Mathematica
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：23
- 期：1
- 页码：293-362
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics, general;
- 出版者：Springer International Publishing
- ISSN：1420-9020
- 卷排序：23
文摘
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 Poincaré duality of Salvatore and Lurie to the setting of stratified spaces—this is a nonabelian version of the Poincaré duality given by intersection homology. We pay special attention to the simple case of singular manifolds whose singularity datum is a properly embedded submanifold, and give a further simplified algebraic characterization of these homology theories. In the case of 3-manifolds with one-dimensional submanifolds, these structures give rise to knot and link homology theories.