On the topology of a boolean representable simplicial complex

Stuart Margolis; John Rhodes; Pedro V. Silva

On the topology of a boolean representable simplicial complex

Combinatorics 2015-10-20 v1 Algebraic Topology

Authors: Stuart Margolis , John Rhodes , Pedro V. Silva

Abstract

It is proved that fundamental groups of boolean representable simplicial complexes are free and the rank is determined by the number and nature of the connected components of their graph of flats for dimension $\geq 2$ . In the case of dimension 2, it is shown that boolean representable simplicial complexes have the homotopy type of a wedge of spheres of dimensions 1 and 2. Also in the case of dimension 2, necessary and sufficient conditions for shellability and being sequentially Cohen-Macaulay are determined. Complexity bounds are provided for all the algorithms involved.

Keywords

homotopy groups algebraic topology simplicial complexes

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@article{arxiv.1510.05113,
  title  = {On the topology of a boolean representable simplicial complex},
  author = {Stuart Margolis and John Rhodes and Pedro V. Silva},
  journal= {arXiv preprint arXiv:1510.05113},
  year   = {2015}
}

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30 pages

On the topology of a boolean representable simplicial complex

Abstract

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