Timeline for Simple proof for property R conjecture
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jul 25, 2018 at 14:41 | answer | added | Ian Agol | timeline score: 12 | |
| Oct 19, 2016 at 3:32 | comment | added | Ian Agol | I forgot that also Marty Scharlemann had a reworking of the proof of Property R (or rather the Poenaru conjecture) that was somewhat simpler (doing away with taut foliations, but using sutured manifold hierarchies). ams.org/mathscinet-getitem?mr=992331 I still wouldn't call the proof "simple" (neither is Gordon-Luecke's proof). | |
| Jun 10, 2015 at 1:47 | vote | accept | user156937 | ||
| Jun 9, 2015 at 12:15 | comment | added | Ian Agol | @MikeMiller: yes, since 0-framed surgery is irreducible, the Seiberg-Witten Floer homology is non-trivial. | |
| Jun 9, 2015 at 12:02 | comment | added | mme | @IanAgol: Thanks for the correction. I guess the interdependence comes from the use of the foliations constructed in "Foliations and the topology of 3-manifolds"? | |
| Jun 9, 2015 at 8:52 | answer | added | Ian Agol | timeline score: 17 | |
| Jun 9, 2015 at 8:45 | comment | added | Ian Agol | @MikeMiller: true, but these results actually depend on Property R. | |
| Jun 9, 2015 at 4:54 | comment | added | mme | You can prove this (indeed, a more general theorem that $r$-surgery on a knot $K \subset S^3$ is diffeomorphic to $r$-surgery on the unknot iff $K$ is the unknot, $r \in \mathbb Q$) using monopole Floer homology or Heegaard Floer homology; see "Monopoles and Lens spaces surgeries" or "Holomorphic disks and genus bounds" respectively. As far as I know, though, this is in a much different direction than Agol and Wise's work. | |
| Jun 9, 2015 at 4:19 | history | edited | user156937 | CC BY-SA 3.0 |
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| Jun 9, 2015 at 3:29 | comment | added | Igor Rivin | Where by "Gabber" I assume you mean "Gabai". | |
| Jun 9, 2015 at 2:39 | history | asked | user156937 | CC BY-SA 3.0 |