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Stellar Stratifications on Classifying Spaces

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arxiv 1804.11274 v2 pith:LBIZDRTK submitted 2018-04-30 math.AT

Dai Tamaki , Hiro Lee Tanaka This is my paper · ORCID
classification math.AT
keywords stellarclassifyingcomplexescylindricallyfinitenormalspacesanalogue
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abstract

We extend Bj\"orner's characterization of the face poset of finite CW complexes to a certain class of stratified spaces, called cylindrically normal stellar complexes. As a direct consequence, we obtain a discrete analogue of cell decompositions in smooth Morse theory, by using the classifying space model introduced in arXiv:1612.08429. As another application, we show that the exit-path simplicial set $\mathrm{Exit}(X)$ of a finite cylindrically normal CW stellar complex $X$ is a quasicategory.

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Cited by 1 Pith paper

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  1. Stratified Homotopy Theory

    math.AT 2019-08 accept novelty 7.0 of 10

    A model-categorical foundation for filtered and stratified spaces and simplicial sets is constructed, with filtered homotopy groups and a filtered Whitehead theorem, while the full filtered Kan-Quillen equivalence rem...

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