Geodesic
On normal subgroups of the braided Thompson groups
Matthew C.B. Zaremsky1 orcid
1University of Albany (SUNY), USA
Groups, geometry, and dynamics, Tome 12 (2018) no. 1, pp. 65-92

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DOI

We inspect the normal subgroup structure of the braided Thompson groups Vbr​ and Fbr​. We prove that every proper normal subgroup of Vbr​ lies in the kernel of the natural quotient Vbr​↠V, and we exhibit some families of interesting such normal subgroups. For Fbr​, we prove that for any normal subgroup N of Fbr​, either N is contained in the kernel of Fbr​↠F, or else N contains [Fbr​,Fbr​]. We also compute the Bieri–Neumann–Strebel invariant Σ1(Fbr​), which is a useful tool for understanding normal subgroups containing the commutator subgroup.
DOI : 10.4171/ggd/438
Classification : 20-XX
Mots-clés : Thompson group, braid group, BNS-invariant, finiteness properties

Matthew C.B. Zaremsky  1

1 University of Albany (SUNY), USA 
Matthew C.B. Zaremsky. On normal subgroups of the braided Thompson groups. Groups, geometry, and dynamics, Tome 12 (2018) no. 1, pp. 65-92. doi: 10.4171/ggd/438
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     title = {On normal subgroups of the braided {Thompson} groups},
     journal = {Groups, geometry, and dynamics},
     pages = {65--92},
     year = {2018},
     volume = {12},
     number = {1},
     doi = {10.4171/ggd/438},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/438/}
}
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