Timeline for Quantitative word problem for 3-manifold groups
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Jan 30, 2021 at 18:41 | answer | added | Ian Agol | timeline score: 4 | |
| Dec 23, 2020 at 16:22 | comment | added | HJRW | @dodd -- presumably you are worried about the compact case with boundary, rather than the non-compact case addressed in YCor's comment. Compact 3-manifolds with boundary are retracts of their doubles, which are closed. This usually makes it easy to reduce from the compact case to the closed case. | |
| Dec 20, 2020 at 19:11 | comment | added | Ian Agol | A uniform treatment of the word problem in 3-manifold groups is given here: arxiv.org/abs/1609.06253 However, the issues of computational complexity are not addressed. | |
| Dec 20, 2020 at 16:48 | review | Suggested edits | |||
| Dec 20, 2020 at 18:58 | |||||
| Dec 19, 2020 at 3:29 | vote | accept | Ben Cooper | ||
| Dec 19, 2020 at 3:29 | comment | added | Ben Cooper | I've tried to make the statement at the end more precise | |
| Dec 19, 2020 at 3:28 | history | edited | Ben Cooper | CC BY-SA 4.0 |
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| Dec 19, 2020 at 0:49 | answer | added | Moishe Kohan | timeline score: 11 | |
| Dec 18, 2020 at 21:57 | comment | added | markvs | So what is the answer? | |
| Dec 18, 2020 at 21:56 | comment | added | YCor | @dodd using infinite connected sums it's easy to product non-closed 3-manifold groups that are not computable. | |
| Dec 18, 2020 at 21:50 | history | edited | YCor |
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| Dec 18, 2020 at 19:55 | comment | added | markvs | Is the 3-manifold closed? | |
| Dec 18, 2020 at 19:04 | comment | added | YCor | I don't understand the last paragraph: there should be a quantifier for $l$. | |
| Dec 18, 2020 at 19:02 | comment | added | YCor | In SOL the Dehn function is exponential but the word problem is very efficiently solvable. The assertion, sometimes heard, that the Dehn function is a measure of the complexity of the word problem is quite misleading. Actually, I'd tend to believe that the $\pi_1$ of every compact 3-fold (possibly with boundary) embeds into a group with quadratic Dehn function (but I don't think this is the easiest/ most efficient approach to algorithms). | |
| Dec 18, 2020 at 17:02 | comment | added | Moishe Kohan | If you restrict to irreducible 3-manifolds then "most" have automatic fundamental groups (the only exceptions are Sol and Nil-manifolds). This gives you some "explicit" bounds. See "Word processing in groups." | |
| Dec 18, 2020 at 16:47 | history | asked | Ben Cooper | CC BY-SA 4.0 |