Some remarks on PL collapsible covers of 2-dimensional polyhedra

Eugenio Borghini

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arXiv · 1802.01538

Some remarks on PL collapsible covers of 2-dimensional polyhedra

Eugenio Borghini

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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.

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Eugenio Borghini. 2018-02-05. Some remarks on PL collapsible covers of 2-dimensional polyhedra. https://arxiv.org/abs/1802.01538

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