Subdivision-based homotopy equivalence of digital circles
[EN] 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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/221843 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/221843 |
| Access Level: | acceso abierto |
| Palabra clave: | Digital circle subdivision subdivision-based homotopy equivalence digital fundamental group |
| Sumario: | [EN] 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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