Ioana-Claudia Lazar: Systolic simplicial complexes are collapsible, p.229-236


We find necessary and sufficient conditions for the collapsibility of a finite simplicial complex of arbitrary finite dimension. Our main result states that any finite systolic simplicial complex of finite dimension, collapses to a point. A simplicial complex is systolic if it is simply connected, connected and locally $6$-large. Local $6$-largeness is a simple combinatorial condition defined in terms of links in the complex. Our proof is based on the fact that any cycle in a systolic complex has a van Kampen diagram of minimal area whose disk is itself systolic.

Key Words: Simplicial complex, star of a simplex, link of a simplex, systole of a complex, locally $6$-large, systolic, van Kampen diagram, collapsibility.

2000 Mathematics Subject Classification: Primary: 05C99;
Secondary: 05C75.

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