Proper topological complexity
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913663327141888 |
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| author | Garcia-Calcines, Jose M. Murillo, Aniceto |
| author_facet | Garcia-Calcines, Jose M. Murillo, Aniceto |
| contents | We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe'' area. To make it a homotopy functorial invariant we characterize it as a particular instance of the exterior sectional category of an exterior map, an invariant of the exterior homotopy category which is also deeply analyzed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16679 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Proper topological complexity Garcia-Calcines, Jose M. Murillo, Aniceto Algebraic Topology 55M30, 55P57 We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe'' area. To make it a homotopy functorial invariant we characterize it as a particular instance of the exterior sectional category of an exterior map, an invariant of the exterior homotopy category which is also deeply analyzed. |
| title | Proper topological complexity |
| topic | Algebraic Topology 55M30, 55P57 |
| url | https://arxiv.org/abs/2407.16679 |