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Surgeries on periodic links and homology of periodic 3-manifolds
| Content Provider | Scilit |
|---|---|
| Author | Przytycki, Józef H. Sokolov, Maxim V. |
| Copyright Year | 2001 |
| Description | Fix a prime integer p. We show that a closed orientable 3-manifold M admits an action of $Z_{p}$ with the fixed point set $S^{1}$ if and only if M can be obtained as the result of surgery on a p-periodic framed link L and $Z_{p}$ acts freely on the components of L. We prove a similar theorem for free $Z_{p}$-actions. As an interesting application, we prove the following, rather unexpected result: for any M as above and for any odd prime p, $H_{1}$(M, $Z_{p}$) ≠ $Z_{p}$. We also prove a similar criterion of 2-periodicity for rational homology 3-spheres. |
| Related Links | http://arxiv.org/pdf/math/0002231 http://arxiv.org/abs/math/0002231 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2D027F7D38CCDEBFDCD0E409ED2AED9B/S0305004101005308a.pdf/div-class-title-surgeries-on-periodic-links-and-homology-of-periodic-3-manifolds-div.pdf |
| Ending Page | 307 |
| Page Count | 13 |
| Starting Page | 295 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004101005308 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 2 |
| Volume Number | 131 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2001-09-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
