Timeline for What are some of the big open problems in 3-manifold theory?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Feb 28, 2012 at 1:18 | comment | added | Lee Mosher | Thanks for the welcome. I realize I'm a little late to the party, but hey, it's still fun. | |
| Feb 27, 2012 at 21:37 | comment | added | Ryan Budney | Welcome to MO, Lee. Yeah, I don't think my opinion in this regard is particularly popular and you're not the first person to disagree with me. | |
| Feb 27, 2012 at 21:06 | comment | added | Lee Mosher | I must respectfully disagree. In light of the Kahn-Markovic theorem, the importance of VFC has been heightened even further. Combining K-M with Thurston's dichotomy for surface subgroups (every surface subgroup of an $H^3$-manifold group is either undistorted or $\pi_1$ of a virtual fiber) VFC is now known to be equivalent to the following: The fundamental group of every closed hyperbolic 3-manifold contains a distorted surface group. I believe it is true (someone correct me if I'm wrong) that the surface subgroups constructed by K-M are all undistorted. | |
| Aug 25, 2010 at 17:14 | comment | added | Ryan Budney | I'd argue you made the point that some of Agol's work is applicable. VFC may have been part of his interest but it's not VFC that's actually been applied. But that's a small point. | |
| Aug 25, 2010 at 16:19 | comment | added | HJRW | On the other hand, the question didn't ask for opinions as to which problem is 'the biggest'! Actually, I'm interested in your opinion and I don't disagree that (the subject of) 3-manifolds needs to look outwards. Which is why I wanted to point out that some of the problems already mentioned are indeed 'applicable'. | |
| Aug 25, 2010 at 7:04 | comment | added | Ryan Budney | Somehow an argument making the point of the interconnectedness of things in a thread which has the intent to artificially single-out individual "big" problems seems contrary to the point. :) My point being largely that 3-manifold theory's future growth should largely be outward to subjects bordering-on 3-manifold theory. And refining geometrization to make it more easily applicable and useful. | |
| Aug 25, 2010 at 5:23 | comment | added | HJRW | Ryan, I think your distinction is a little artificial. For instance, I would rate Friedl and Vidussi's proof that a 3-manifold $N$ is fibred if and only if $S^1 \times N$ is symplectic as one of the most attractive examples of 'a strong connection between the geometric perspective on 3-manifolds and other perspectives'. Their proof made crucial use of Agol's work on the Virtual Fibring Conjecture. | |
| Aug 25, 2010 at 4:44 | history | edited | Ryan Budney | CC BY-SA 2.5 |
expand topic
|
| Aug 25, 2010 at 4:22 | history | answered | Ryan Budney | CC BY-SA 2.5 |