2018/04/30 by Dai Tamaki, Hiro Lee Tanaka, Tamaki, Dai +1
Mathematics · #55U40 (Secondary) #57N80 (Primary) #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:55U40 #msc:57N80
paper · pdf · doi:10.48550/arxiv.1804.11274
23 pages. v2 updated according to referee's comments
arxiv created 2018/09/14 · arxiv updated 2018/09/18
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 arXiv:1612.08429. As another application, we show that the exit-path simplicial set Exit(X) of a finite cylindrically normal CW stellar complex X is a quasicategory.