Factorization homology of stratified spaces

• David Ayala ^[1] ; John Francis ^[2] ; Hiro Lee Tanaka ^[3]
  1. [1] Montana State University

     Montana State University

     Estados Unidos

     
  2. [2] Northwestern University

     Northwestern University

     Township of Evanston, Estados Unidos

     
  3. [3] Harvard University

     Harvard University

     City of Cambridge, Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 1, 2017, págs. 293-362
• Idioma: inglés
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• Resumen

  • 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 strati- fied 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.