Djordje Baralic, Ioana-Claudia Lazar: Finite and locally finite simplicial complexes of nonpositive curvature p. 205-216


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.

Key Words: local $6$-largeness, directed geodesic, Morse matching, collapsibility, arborescent structure

2010 Mathematics Subject Classification: Primary 05C99, Secondary 05C75