Semi-coarse Spaces: Fundamental Groupoid and the van Kampen Theorem
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916643439902720 |
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| author | Treviño-Marroquín, Jonathan |
| author_facet | Treviño-Marroquín, Jonathan |
| contents | In algebraic topology, the fundamental groupoid is a classical homotopy invariant which is defined using continuous maps from the closed interval to a topological space. In this paper, we construct a semi-coarse version of this invariant, using as paths a finite sequences of maps from $\mathbb{Z}_1$ to a semi-coarse space, connecting their tails through semi-coarse homotopy. In contrast to semi-coarse homotopy groups, this groupoid is not necessarily trivial for coarse spaces, and, unlike coarse homotopy, it is well-defined for general semi-coarse spaces. In addition, we show that the semi-coarse fundamental groupoid which we introduce admits a version of the Van Kampen Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08874 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semi-coarse Spaces: Fundamental Groupoid and the van Kampen Theorem Treviño-Marroquín, Jonathan Algebraic Topology General Topology In algebraic topology, the fundamental groupoid is a classical homotopy invariant which is defined using continuous maps from the closed interval to a topological space. In this paper, we construct a semi-coarse version of this invariant, using as paths a finite sequences of maps from $\mathbb{Z}_1$ to a semi-coarse space, connecting their tails through semi-coarse homotopy. In contrast to semi-coarse homotopy groups, this groupoid is not necessarily trivial for coarse spaces, and, unlike coarse homotopy, it is well-defined for general semi-coarse spaces. In addition, we show that the semi-coarse fundamental groupoid which we introduce admits a version of the Van Kampen Theorem. |
| title | Semi-coarse Spaces: Fundamental Groupoid and the van Kampen Theorem |
| topic | Algebraic Topology General Topology |
| url | https://arxiv.org/abs/2404.08874 |