Timeline for Is there a procedure for obtaining all knots in S^3?
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Mar 10, 2017 at 9:42 | history | edited | CommunityBot |
replaced http://upload.wikimedia.org/ with https://upload.wikimedia.org/
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| Jan 15, 2015 at 0:43 | history | edited | Ryan Budney | CC BY-SA 3.0 |
Fix broken links, add one more example
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| Aug 5, 2010 at 6:25 | comment | added | Ryan Budney | xfig, it comes with Linux. | |
| Aug 5, 2010 at 2:06 | comment | added | Victor Protsak | Ryan, what software did you use for the pictures? | |
| Aug 4, 2010 at 9:04 | comment | added | Ryan Budney | Again with this, there's infinitely many indecomposables. | |
| Aug 4, 2010 at 9:03 | comment | added | Ryan Budney | Hyperbolic knots and links have further decompositions but I'm not aware of any that decompose them into knots and links. A classic and closely-related decomposition to the one above is sometimes called the "rational-tangle decomposition" or the "$\mathbb Z_2$-equivariant JSJ-decomposition." It is what you get when you look at the JSJ-decomposition of the $\mathbb Z_2$-branched cover of $S^3$, branched over the link. www-bcf.usc.edu/~fbonahon/Research/Preprints/BonSieb.pdf | |
| Aug 4, 2010 at 7:59 | comment | added | Peter Samuelson | Ah, I should have looked at Wikipedia before commenting. It looks like there's much more information here arxiv4.library.cornell.edu/abs/math/0506523 :-) And it looks like the answer to the question in the comment above is no... | |
| Aug 4, 2010 at 7:50 | comment | added | Ryan Budney | Hyperbolic knots and torus knots are precisely the indecomposables. There's infinitely many of both. | |
| Aug 4, 2010 at 7:37 | comment | added | Peter Samuelson | These are very nice pictures, thanks! Are there finitely many knots that are "indecomposable" in this sense? | |
| Aug 4, 2010 at 7:13 | history | edited | Ryan Budney | CC BY-SA 2.5 |
link
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| Aug 4, 2010 at 7:04 | history | edited | Ryan Budney | CC BY-SA 2.5 |
another picture
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| Aug 4, 2010 at 6:52 | history | undeleted | Ryan Budney | ||
| Aug 4, 2010 at 6:52 | history | edited | Ryan Budney | CC BY-SA 2.5 |
added 456 characters in body
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| Aug 4, 2010 at 6:45 | history | edited | Ryan Budney | CC BY-SA 2.5 |
less trivial answer; added 14 characters in body
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| Aug 4, 2010 at 6:38 | history | deleted | Ryan Budney | ||
| Aug 4, 2010 at 6:37 | history | answered | Ryan Budney | CC BY-SA 2.5 |