Authors: Baralić, Đorđe 
Lazar, Ioana
Title: A note on the combinatorial structure of finite and locally finite simplicial complexes of nonpositive curvature
Journal: Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
Volume: 59
Issue: 3
First page: 205
Last page: 216
Issue Date: 1-Jan-2016
Rank: M22
ISSN: 1220-3874
Abstract: 
We investigate the collapsibility of systolic finite simplicial complexes of arbitrary dimension. The main tool we use in the proof is discrete Morse theory. We shall consider a convex subcomplex of the complex and project any simplex of the complex onto a ball around this convex subcomplex. These projections will induce a convenient gradient matching on the complex. Besides we analyze the combinatorial structure of both CAT(0) and systolic locally finite simplicial complexes of arbitrary dimensions. We will show that both such complexes possess an arborescent structure. Along the way we make use of certain well known results regarding systolic geometry.
Keywords: Arborescent structure | Collapsibility | Directed geodesic | Local 6-largeness | Morse matching
Publisher: Societatea de Stiinte Matematice din Romani
Project: Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 
Ministry for Science of the Republic of Srpska, Grant 19/6-020/961120/14

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