Abstract
We develop a theory of conically smooth stratified spaces and their smooth moduli, including a notion of classifying maps for tangential structures. We characterize continuous space-valued sheaves on these conically smooth stratified spaces in terms of tangential data, and we similarly characterize 1-excisive invariants of stratified spaces. These results are based on the existence of open handlebody decompositions for conically smooth stratified spaces, an inverse function theorem, a tubular neighborhood theorem, an isotopy extension theorem, and functorial resolutions of singularities to smooth manifolds with corners.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 903-1028 |
| Number of pages | 126 |
| Journal | Advances in Mathematics |
| Volume | 307 |
| DOIs | |
| State | Published - Feb 5 2017 |
Funding
DA was partially supported by ERC adv. grant no. 228082, by the NSF under Award 0902639, and by the NSF Award 0932078 000 while residing at the MSRI for Spring 2014. JF was supported by the NSF under Award 0902974 and Award 1207758; part of this paper was written while JF was a visitor at Paris 6 in Jussieu. HLT was supported by an NSF Graduate Research Fellowship, by the Northwestern University Office of the President, by the Centre for Quantum Geometry of Moduli Spaces, and by the NSF under Award DMS-1400761.
Keywords
- Configuration spaces
- Constructible sheaves
- Handlebodies
- Ran spaces
- Resolution of singularities
- Singular manifolds
- Stratified spaces
- Topological quantum field theory
- ∞-Categories
ASJC Scopus subject areas
- General Mathematics