2018/04/12 by Nima Hoda, Hoda, Nima
Computer Science · Mathematics · #05C12 #20F67 #55P20 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Primary 20F65 #Secondary 57Q15 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1804.04630
openalex publication_date 2018/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a discrete Morse-theoretic method for proving that a regular CW complex is homeomorphic to a sphere. We use this method to define bisimplices, the cells of a class of regular CW complexes we call bisimplicial complexes. The 1-skeleta of bisimplices are complete bipartite graphs making them suitable in constructing higher dimensional skeleta for bipartite graphs. We show that the flag bisimplicial completion of a finite bipartite bi-dismantlable graph is collapsible. We use this to show that the flag bisimplicial completion of a quadric complex is contractible and to construct a compact K(G,1) for G a torsion-free quadric group.