Geometry of collapsing and free deformation retraction

Alexey Gorelov

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arXiv · 2103.16464

Geometry of collapsing and free deformation retraction

Alexey Gorelov

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Abstract

We show that a compact polyhedron $P$ collapses to a subpolyhedron $Q$ if and only if it admits a piecewise-linear free deformation retraction onto $Q$. 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.

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Alexey Gorelov. 2021-03-30. Geometry of collapsing and free deformation retraction. https://arxiv.org/abs/2103.16464

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