2018/02/05 by Eugenio Borghini, Borghini, Eugenio · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #20F05 #52B99 #55M30 #57M20 #57Q05 #Algebraic Topology (math.AT) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Microtubule and mitosis dynamics #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.1802.01538
openalex publication_date 2018/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze the topology and geometry of a polyhedron of dimension 2 according to the minimum size of a cover by PL collapsible polyhedra. We provide partial characterizations of the polyhedra of dimension 2 that can be decomposed as the union of two PL collapsible subpolyhedra in terms of their simple homotopy type and certain local properties. In the process, a special class of polyhedra of dimension 2 appears naturally. We give a combinatorial description of the spaces in this class, which includes all closed surfaces and the complexes associated to one-relator presentations.