Some remarks on PL collapsible covers of 2-dimensional polyhedra
Geometric Topology
2018-02-06 v1 Algebraic Topology
Abstract
We analyze the topology and geometry of a polyhedron of dimension 2 according to the minimum size of a cover by PL collapsible polyhedra. We provide partial characterizations of the polyhedra of dimension 2 that can be decomposed as the union of two PL collapsible subpolyhedra in terms of their simple homotopy type and certain local properties. In the process, a special class of polyhedra of dimension 2 appears naturally. We give a combinatorial description of the spaces in this class, which includes all closed surfaces and the complexes associated to one-relator presentations.
Keywords
Cite
@article{arxiv.1802.01538,
title = {Some remarks on PL collapsible covers of 2-dimensional polyhedra},
author = {Eugenio Borghini},
journal= {arXiv preprint arXiv:1802.01538},
year = {2018}
}
Comments
11 pages, 1 figure