Compact aspherical solenoids
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2010
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| _version_ | 1866913920147521536 |
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| author | Belk, James Forrest, Bradley |
| author_facet | Belk, James Forrest, Bradley |
| contents | We consider compact, aspherical solenoids obtained as the inverse limit of a system of CW~complexes and covering maps. This includes $P$-adic solenoids, as well as the universal hyperbolic solenoid of Teichmüller theory. Using ideas from shape theory, we classify maps between such solenoids up to homotopy, and we prove a Dehn-Nielsen-type theorem for self-homotopy equivalences of such a solenoid. This generalizes a result of Odden regarding the universal hyperbolic solenoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1009_5716 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | Compact aspherical solenoids Belk, James Forrest, Bradley Geometric Topology Algebraic Topology 55P55 (Primary) 55P10, 30F60, 37B45 (Secondary) We consider compact, aspherical solenoids obtained as the inverse limit of a system of CW~complexes and covering maps. This includes $P$-adic solenoids, as well as the universal hyperbolic solenoid of Teichmüller theory. Using ideas from shape theory, we classify maps between such solenoids up to homotopy, and we prove a Dehn-Nielsen-type theorem for self-homotopy equivalences of such a solenoid. This generalizes a result of Odden regarding the universal hyperbolic solenoid. |
| title | Compact aspherical solenoids |
| topic | Geometric Topology Algebraic Topology 55P55 (Primary) 55P10, 30F60, 37B45 (Secondary) |
| url | https://arxiv.org/abs/1009.5716 |