Geometry of collapsing and free deformation retraction
Geometric Topology
2026-03-09 v2
Abstract
We show that a compact polyhedron collapses to a subpolyhedron if and only if it admits a piecewise-linear free deformation retraction onto . We also consider further possibilities for invariant characterisations of collapsibility in terms of metrics; in this connection, we provide a partial correction to Isbell's claim that every injective metric space is freely contractible, and present a counterexample to a step in the original argument.
Keywords
Cite
@article{arxiv.2103.16464,
title = {Geometry of collapsing and free deformation retraction},
author = {Alexey Gorelov},
journal= {arXiv preprint arXiv:2103.16464},
year = {2026}
}
Comments
27 pages, 6 figures. In the present version, the original text has been significantly revised and section 5 has been added