Local structures on stratified spaces

David Ayala, John Francis*, Hiro Lee Tanaka

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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 languageEnglish (US)
Pages (from-to)903-1028
Number of pages126
JournalAdvances in Mathematics
StatePublished - Feb 5 2017


  • Configuration spaces
  • Constructible sheaves
  • Handlebodies
  • Ran spaces
  • Resolution of singularities
  • Singular manifolds
  • Stratified spaces
  • Topological quantum field theory
  • ∞-Categories

ASJC Scopus subject areas

  • Mathematics(all)


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