A four-term exact sequence of fundamental groups of orbit configuration spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917412320837632 |
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| author | Roushon, S. K. |
| author_facet | Roushon, S. K. |
| contents | We deduce that the fundamental groups of the orbit configuration spaces of an effective and properly discontinuous action of a discrete group on a connected aspherical 2-manifold, with isolated fixed points, fit into a four-term exact sequence. This comes as a consequence of the four-term exact sequence of orbifold pure braid groups ([18], [11] and [19]). The proof relates these two exact sequences and also draws a new consequence (Corollary 2.3) on the later one. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_19853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A four-term exact sequence of fundamental groups of orbit configuration spaces Roushon, S. K. Geometric Topology Algebraic Topology Primary 55R80, 55P65, Secondary 20F99, 57R18 We deduce that the fundamental groups of the orbit configuration spaces of an effective and properly discontinuous action of a discrete group on a connected aspherical 2-manifold, with isolated fixed points, fit into a four-term exact sequence. This comes as a consequence of the four-term exact sequence of orbifold pure braid groups ([18], [11] and [19]). The proof relates these two exact sequences and also draws a new consequence (Corollary 2.3) on the later one. |
| title | A four-term exact sequence of fundamental groups of orbit configuration spaces |
| topic | Geometric Topology Algebraic Topology Primary 55R80, 55P65, Secondary 20F99, 57R18 |
| url | https://arxiv.org/abs/2502.19853 |