Stellar Stratifications on Classifying Spaces

Dai Tamaki; Hiro Lee Tanaka

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arXiv · 1804.11274

Stellar Stratifications on Classifying Spaces

Dai Tamaki·Hiro Lee Tanaka

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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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Dai Tamaki, Hiro Lee Tanaka. 2018-04-30. Stellar Stratifications on Classifying Spaces. https://arxiv.org/abs/1804.11274

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