Timeline for Diffeomorphism of 3-manifolds
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| S May 4, 2022 at 7:40 | history | suggested | The Amplitwist | CC BY-SA 4.0 |
fixed broken link to springerlink.com
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| May 4, 2022 at 4:19 | review | Suggested edits | |||
| S May 4, 2022 at 7:40 | |||||
| Dec 18, 2009 at 17:56 | comment | added | Ian Agol | @ algori: he's claiming that simple homotopy equivalent manifolds are homeomorphic. | |
| Dec 17, 2009 at 16:21 | comment | added | algori | Agol, Tim -- I can't access Turaev's paper right now, but if he claims that a homotopy equivalence is a simple homotopy equivalence for 3-manifolds, this would seem a little strange, since for lens spaces this is false: L(7,1) and L(7,2) are homotopy equivalent, but have different simple homotopy types. | |
| Dec 16, 2009 at 2:58 | comment | added | Tim Perutz | Agol gets the green box for pointing Turaev's paper which, alongside his 1988 paper "Homeomorphisms of geometric three-dimensional manifolds", MR0940851, apparently answers both questions affirmatively. However, Turaev's argument draws together threads that Paul, Daniel, John, algori, Henry and Ryan mentioned - in particular, Waldhausen's work on the Haken case. Thanks to all. | |
| Dec 15, 2009 at 23:56 | vote | accept | Tim Perutz | ||
| Dec 15, 2009 at 21:34 | comment | added | Ryan Budney | The main issue is the connect-sum decomposition, no? Ie: oriented simple homotopy equivalent 3-manifolds have oriented simple-homotopy equivalent prime summands. Once you're past that JSJ + geometrization tools take over. | |
| Dec 15, 2009 at 20:20 | history | edited | Ian Agol | CC BY-SA 2.5 |
added 349 characters in body
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| Dec 15, 2009 at 18:32 | history | answered | Ian Agol | CC BY-SA 2.5 |