2014/11/05 by Patricia Hersh, Hersh, Patricia
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Homotopy and Cohomology in Algebraic Topology #Advanced Topology and Set Theory
paper · pdf · doi:10.48550/arxiv.1411.1296
Anders Bjorner characterized which finite graded partially ordered sets arise as the posets of closure relations on cells of a finite, regular CW complex. His characterization of these "CW posets" required each open interval (0,u) to have order complex homeomorphic to a sphere of dimension rk(u)-2. Work of Danaraj and Klee showed that sufficient conditions were for the poset to be thin and shellable. The proof of the Poincare Conjecture enables the requirement of shellability to be replaced by the homotopy Cohen-Macaulay property. This expands the range of tools that may be used to prove a poset is a CW poset.