Geometry of collapsing and free deformation retraction
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2021
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| Acceso en línea: | |
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| _version_ | 1866908868892688384 |
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| author | Gorelov, Alexey |
| author_facet | Gorelov, Alexey |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_16464 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Geometry of collapsing and free deformation retraction Gorelov, Alexey Geometric Topology 57Q05, 57Q25 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. |
| title | Geometry of collapsing and free deformation retraction |
| topic | Geometric Topology 57Q05, 57Q25 |
| url | https://arxiv.org/abs/2103.16464 |