Timeline for Isomorphism of semidirect products of surface groups
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 10, 2020 at 21:22 | comment | added | Moishe Kohan | It is likely to be undecidable for the same reason that the braid factorization is undecidable, check arxiv.org/pdf/math/0511153.pdf | |
| Aug 10, 2020 at 7:15 | answer | added | jonathan | timeline score: 2 | |
| Aug 8, 2020 at 21:57 | comment | added | Ian Agol | Nick Salter has found examples of surface-by-surface groups that fiber in different ways. However, I don't know if these are split.msp.org/gt/2015/19-5/p10.xhtml | |
| Aug 8, 2020 at 11:29 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
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| Aug 8, 2020 at 10:52 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
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| Aug 8, 2020 at 10:51 | comment | added | Francesco Polizzi | @DerekHolt: Thank you for the suggestions. Actually, as I said, in my example the abelianizations (and so the abelian invariants) are the same in both cases. As you remarked, there is a large number of generators, so trying to construct an isomorphism by hand seems to be difficult (at least, for me). | |
| Aug 8, 2020 at 9:17 | comment | added | Derek Holt | Computationally, since the groups have solvable word problem, it is possible to check whether a sequence of generator images induces an isomorphism, so one can search for an isomorphism. One can also compute varionus invariants (such as the abelian invariants) and try and prove that they are not isomorphic. Both of those processes are much more difficult when there are large numbers of generators, which appears to be the case in this example. | |
| Aug 8, 2020 at 8:34 | history | asked | Francesco Polizzi | CC BY-SA 4.0 |