Local structures on stratified spaces

David Ayala; John Francis; Hiro Lee Tanaka

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arXiv · 1409.0501

Local structures on stratified spaces

David Ayala·John Francis·Hiro Lee Tanaka

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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.

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David Ayala, John Francis, Hiro Lee Tanaka. 2014-09-01. Local structures on stratified spaces. https://arxiv.org/abs/1409.0501

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