Subdivision-based homotopy equivalence of digital circles
A direct translation of the notion of homotopy equivalence from algebraic topology to digital images leads to a much more rigid definition in the context of digital topology. This results in two digital circles of different radii being not homotopic. A more suitable idea of equivalences, called &quo...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Universitat Politècnica de València
2025-04-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/22288 |
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| Summary: | A direct translation of the notion of homotopy equivalence from algebraic topology to digital images leads to a much more rigid definition in the context of digital topology. This results in two digital circles of different radii being not homotopic. A more suitable idea of equivalences, called "subdivision-based homotopy equivalence" which is introduced by Lupton et al., involves the concept of subdivision of digital images. We prove that, in this sense, any digital circle is subdivision-based homotopic to the Diamond, the prototypical digital circle of radius 1, which implies, as a consequence, that the fundamental group of any digital circle is isomorphic to Z. |
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| ISSN: | 1576-9402 1989-4147 |