Abstract
We extend Björner’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 Nanda et al (Discrete Morse theory and classifying spaces, arXiv:1612.08429 [15]). As another application, we show that the exit-path category \(\mathsf {Exit}(X)\), in the sense of Lurie (Higher algebra, http://www.math.harvard.edu/~lurie/papers/HA.pdf [11]), of a finite cylindrically normal CW stellar complex X is a quasi-category.
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References
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Acknowledgements
This project started when the authors were invited to the IBS Center for Geometry and Physics in Pohang in December, 2016. We would like to thank the center for invitation and the nice working environment.
The contents of this paper were presented by the first author during the 7th East Asian Conference on Algebraic Topology held at Mohali, India, in December, 2017. He is grateful to the local organizers for the invitation to the conference and the hospitality of IISER Mohali.
The authors would like to thank the anonymous referee whose valuable suggestions improved expositions and made this paper more readable.
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Tamaki, D., Tanaka, H.L. (2019). Stellar Stratifications on Classifying Spaces. In: Singh, M., Song, Y., Wu, J. (eds) Algebraic Topology and Related Topics. Trends in Mathematics. Birkhäuser, Singapore. https://doi.org/10.1007/978-981-13-5742-8_15
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DOI: https://doi.org/10.1007/978-981-13-5742-8_15
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