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Medientyp:
E-Artikel
Titel:
Systolic simplicial complexes are collapsible
Beteiligte:
Lazăr, Ioana-Claudia
Erschienen:
Societatea de Ştiinţe Mathematice Din România, 2013
Erschienen in:
Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, 56 (104) (2013) 2, Seite 229-236
Sprache:
Englisch
ISSN:
1220-3874;
2065-0264
Entstehung:
Anmerkungen:
Beschreibung:
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.