Local structures on stratified spaces

By David Ayala, J. Francis, Hiro Tanaka. 2014

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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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f8a561139efd36d728dd5454093c97ba0ee084c1