Timeline for What are some of the big open problems in 3-manifold theory?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Sep 11, 2021 at 1:17 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Jun 11, 2018 at 11:03 | history | edited | IJL | CC BY-SA 4.0 |
edited body
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| May 29, 2013 at 10:08 | comment | added | HJRW | Ryan - your comment prompted me to add an update. | |
| May 29, 2013 at 10:07 | comment | added | HJRW | Fernando - you're right, and I've updated the statement accordingly. | |
| May 29, 2013 at 10:06 | history | edited | HJRW | CC BY-SA 3.0 |
Added update on the proofs of these conjectures!
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| May 29, 2013 at 6:17 | comment | added | Ryan Budney | @Fernando: traditionally in statements of theorems like this, spheres and projective planes are discounted. On another topic, this answer is pretty dated now. These aren't open problems anymore. | |
| May 29, 2013 at 3:43 | comment | added | Fernando Muro | SSC is trivially true, isn't it? The trivial group is the fundamental group of the sphere. | |
| May 29, 2013 at 2:17 | history | edited | John Pardon | CC BY-SA 3.0 |
fixed mathscinet links
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| Sep 1, 2010 at 16:12 | comment | added | HJRW | Sorry, I should have said $PD_n$. As you point out below, $PD_3$ could be the same as being a 3-manifold group! | |
| Aug 31, 2010 at 23:58 | history | edited | Ryan Budney | CC BY-SA 2.5 |
missed a hat
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| Aug 27, 2010 at 20:49 | comment | added | HJRW | Igor, you're right to point that out. But I was wondering more about the other side of the question, namely whether `virtually acting on a tree' is invariant under quasi-isometry. I would guess that it isn't, but that it might be under some fairly mild hypotheses like being $PD_3$. | |
| Aug 25, 2010 at 15:32 | comment | added | Igor Belegradek | The question whether "there splitting properties are quasi-isometry invariant" is answered by a theorem of Richard Schwartz: quasi-isometry is equivalent to commensurability for non-uniform lattices in the isometry group of the hyperbolic 3-space. And all uniform lattices are qi to the hyperbolic space. So there seems to be no qi versions of the above conjectures. | |
| Aug 24, 2010 at 22:08 | history | edited | HJRW | CC BY-SA 2.5 |
Fixed typo, added answer to Siegel's comment
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| Aug 24, 2010 at 16:54 | comment | added | Paul Siegel | At the very least I was interested in a little more detail - thanks for providing it! Would it be correct to guess that the "virtually ___ conjecture" problems can be translated into a question about the large scale geometry of the fundamental group? | |
| Aug 22, 2010 at 22:26 | history | edited | HJRW | CC BY-SA 2.5 |
Corrected typos
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| Aug 22, 2010 at 22:07 | history | answered | HJRW | CC BY-SA 2.5 |