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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1712.04572 |
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| _version_ | 1866917489010540544 |
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| author | Hambleton, Ian Hillman, Jonathan A. |
| author_facet | Hambleton, Ian Hillman, Jonathan A. |
| contents | We consider closed topological 4-manifolds $M$ with universal cover ${S^2\times{S^2}}$ and Euler characteristic $χ(M) = 1$. All such manifolds with $π=π_1(M)\cong {\mathbb Z}/4$ are homotopy equivalent. In this case, we show that there are four homeomorphism types, and propose a candidate for a smooth example which is not homeomorphic to the geometric quotient. If $π\cong {\mathbb Z}/2 \times {\mathbb Z}/2$, we show that there are three homotopy types (and between 6 and 24 homeomorphism types). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1712_04572 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Quotients of $S^2\times{S^2}$ Hambleton, Ian Hillman, Jonathan A. Geometric Topology 57M60, 57N70 We consider closed topological 4-manifolds $M$ with universal cover ${S^2\times{S^2}}$ and Euler characteristic $χ(M) = 1$. All such manifolds with $π=π_1(M)\cong {\mathbb Z}/4$ are homotopy equivalent. In this case, we show that there are four homeomorphism types, and propose a candidate for a smooth example which is not homeomorphic to the geometric quotient. If $π\cong {\mathbb Z}/2 \times {\mathbb Z}/2$, we show that there are three homotopy types (and between 6 and 24 homeomorphism types). |
| title | Quotients of $S^2\times{S^2}$ |
| topic | Geometric Topology 57M60, 57N70 |
| url | https://arxiv.org/abs/1712.04572 |