Timeline for Irreducible homology 3-spheres that bound smooth contractible manifolds
Current License: CC BY-SA 3.0
10 events
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| Jun 22, 2022 at 7:16 | history | edited | CommunityBot |
replaced http://front.math.ucdavis.edu/ with https://arxiv.org/abs/
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| Aug 11, 2012 at 19:22 | vote | accept | Igor Belegradek | ||
| Aug 11, 2012 at 12:13 | comment | added | Igor Belegradek | I realize that no infinite family can pass the 11-census but since you mention infinite families of Brieskorn spheres that bound contractible manifolds, you might want to mention Glazner's as well. Also if I may suggest, it would seem helpful to refer to Harriet Moser's paper. | |
| Aug 11, 2012 at 5:13 | comment | added | Ryan Budney | I wasn't aware of the Glazner paper, thanks for pointing it out. It's not clear to me which 3-manifolds embeddings he's constructing, but they appear to be quite large 3-manifolds. Most of my efforts at the moment are focusing on finding embeddings of "small" 3-manifolds into $S^4$. | |
| Aug 11, 2012 at 3:05 | comment | added | Igor Belegradek | Incidentally, Glazner's manifolds in my EDIT embed into $S^4$ but you do not refer to that paper. | |
| Aug 11, 2012 at 2:48 | comment | added | Igor Belegradek | I only asked about Casson-Harer because you mentioned them. Also many thanks for bringing to my attention Harriet Moser's work front.math.ucdavis.edu/0809.1203 which I was not aware of. | |
| Aug 11, 2012 at 2:32 | comment | added | Ryan Budney | As far as I know it's due to me. If you look in the credits for the paper I certainly thank a lot of people for their insights. Danny Ruberman and I talked about these types of manifolds quite a bit so he certainly deserves some credit. Manifold 31 also bounds a contractible 4-manifold. I think there's others in the list -- when I wrote the paper determining whether or not the bounding 4-manifolds was contractible was not a priority, it was at most a step towards finding embeddings in $S^4$. The proof of hyperbolicity is via SnapPea (which is rigorous with the Harriet Moser criterion). | |
| Aug 11, 2012 at 2:20 | comment | added | Igor Belegradek | Thank you! I see manifold 30, but where are the "other examples" you mention? Where do you prove 30 is hyperbolic? Also am I correct that this example is due to yourself (and was not worked out by Casson-Harer)? | |
| Aug 11, 2012 at 2:07 | comment | added | Ryan Budney | The paper is structured sort of like a "workbook" with techniques building up in the beginning, computations in the middle and appendices in the back. This example is manifold 30, on page 22 of the current arXiv version (v4). See also Proposition 2.10 on page 11 for context and details of the argument. Towards the end of the summer I'll upload v5 of the paper -- the paper will be much closer to being complete. | |
| Aug 11, 2012 at 1:09 | history | answered | Ryan Budney | CC BY-SA 3.0 |