Timeline for Algorithm for identifying reducible braids
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Dec 28, 2020 at 22:09 | answer | added | Mark Bell | timeline score: 4 | |
| Mar 3, 2020 at 21:31 | history | edited | YCor |
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| Mar 3, 2020 at 19:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Nov 4, 2019 at 19:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 5, 2019 at 18:16 | answer | added | Ryan Budney | timeline score: 3 | |
| Oct 5, 2019 at 17:57 | comment | added | Just Me | Thanks @RyanBudney, I'll take a look. You seem to make a few mental leaps which I'll have to climb... if you'd like to turn your comments into an answer, I'd gladly accept it. | |
| Oct 5, 2019 at 16:18 | comment | added | Ryan Budney | Mark Bell's "Flipper" appears to be an all-in-one implementation of my initial suggestion, finding the JSJ decomposition of the mapping torus -- although I doubt he uses Regina. flipper.readthedocs.io His software appears well-written. I had looked at some of his software many years ago. These packages appear complete now. | |
| Oct 5, 2019 at 16:12 | comment | added | Ryan Budney | I can imagine a relatively "expensive" way to do it in Regina, looking for incompressible tori in the mapping torus. Have you tried the Bell-Webb algorithm? I have not, but here is an implementation: curver.readthedocs.io/en/master It sounds like it might be exactly what you want, although the authors seem to imply this implementation can be slow, or perhaps memory-intensive. | |
| Oct 4, 2019 at 19:06 | history | edited | Just Me |
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| Oct 4, 2019 at 18:42 | history | edited | Just Me | CC BY-SA 4.0 |
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| Oct 4, 2019 at 18:36 | history | edited | Just Me | CC BY-SA 4.0 |
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| Oct 4, 2019 at 18:33 | comment | added | Just Me | @RyanBudney Thanks for the correction. Do you have a reference giving some kind of algorithm for determining whether an element lies in the image of this map? | |
| Oct 4, 2019 at 17:37 | comment | added | Ryan Budney | Your homomorphism of braid groups, you would either need to make those pure braid groups, or make the $n_i's$ all equal and turn it into a wreath product construction. Regardless, this is the $\pi_1$ map for the $2$-cubes operad's multiplication map. It's discussed in many books and papers that talk about operads, as the cubes operad is perhaps the most heavily studied object in the subject. | |
| Oct 4, 2019 at 15:17 | history | edited | Just Me | CC BY-SA 4.0 |
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| Oct 4, 2019 at 15:08 | history | asked | Just Me | CC BY-SA 4.0 |