Timeline for Topological characterisation for a (closed irreducible) hyperbolic 3-manifold
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jun 17, 2013 at 12:43 | comment | added | Bruno Martelli | A manifold fibering over P^2 with one singular fiber also fibers over S^2 with three singular fibers. This is due to the fact that the orientable fibration over the Mobius strip also fibers over the disc with two singular points of order 2. You can find this in the book of Matveev and Fomenko, with lots of pictures. Concerning the general statement, I suppose that some of the surveys of Cameron Gordon should contain it. See also the paper of Boileau-Porti on orbifolds: mat.uab.es/~porti/main.pdf | |
| Jun 17, 2013 at 12:41 | comment | added | Bruno Martelli | the sentence you wrote is true if you define a SSFS as a 3-manifold that has a Seifert fibration on S^2 with at most 3 singular fibers: such a "weak" notion of SSFS includes everything that has finite pi_1, and everything which contains "immersed tori" but not embedded ones. | |
| Jun 17, 2013 at 12:33 | comment | added | shestipalov | Thanks! That's exactly what I was looking for! Just to confirm, so a compact 3-manifold is not hyperbolic if either it contains an embedded essential surface of non-negative Euler charasteristic or it is a Small Seifert Fibred space? By SSFS do you mean base surface $S^2$ with at most 3 exceptional fibres or do you also include the $P^2$ with at most one exceptional fibre as well? Do you know a text that I could cite making this statement? | |
| Jun 17, 2013 at 12:30 | vote | accept | shestipalov | ||
| Jun 17, 2013 at 11:58 | history | edited | Bruno Martelli | CC BY-SA 3.0 |
fix; added 1 characters in body
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| Jun 17, 2013 at 11:44 | history | edited | Bruno Martelli | CC BY-SA 3.0 |
added 54 characters in body
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| Jun 17, 2013 at 11:34 | history | answered | Bruno Martelli | CC BY-SA 3.0 |