On normal subgroups of the braided Thompson groups.

@article{Zaremsky2014OnNS,
  title={On normal subgroups of the braided Thompson groups.},
  author={Matthew C. B. Zaremsky},
  journal={arXiv: Group Theory},
  year={2014}
}
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 \onto 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 \onto F, or else N contains [Fbr,Fbr]. We also compute the Bieri-Neumann-Strebel invariant Sigma^1(Fbr), which is a useful tool for… 

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References

SHOWING 1-10 OF 19 REFERENCES

Pure braid subgroups of braided Thompson's groups

We describe some properties of braided generalizations of Thompson's groups, introduced by Brin and Dehornoy. We give slightly different characterizations of the braided Thompson's groups $BV$ and

The braided Thompson's groups are of type F∞

Abstract We prove that the braided Thompson’s groups Vbr{V_{\mathrm{br}}} and Fbr{F_{\mathrm{br}}} are of type F∞{\rm F}_{\infty}, confirming a conjecture by John Meier. The proof involves showing

The group of parenthesized braids

Valuations on free resolutions and higher geometric invariants of groups

by free G-modules F~ which are finitely generated for all i < m. If the trivial G-module 7/is of type (FP)m and this is indeed the most interesting situation we say also that the group G is of type

Anti-trees and right-angled Artin subgroups of braid groups

We prove that an arbitrary right-angled Artin group G admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree, and, consequently, into a pure

The algebra of strand splitting. I. A braided version of Thompson's group V

We construct a braided version BV of Thompson’s group V that surjects onto V . The group V is the third of three well known groups F , T and V created by Thompson in the 1960s that have been heavily

Elementary Amenable Subgroups of R. Thompson's Group F

This paper constructs an example of an elementary amenable subgroup up to class (height) omega squared, where omega is the first infinite ordinal.

A minimal non-solvable group of homeomorphisms

Let PLo.I/ represent the group of orientation-preserving piecewise-linear homeo- morphisms of the unit interval which admit finitely many breaks in slope, under the operation of composition. We find

Some Remarks on the Braided Thompson Group BV

Matthew Brin and Patrick Dehornoy independently discovered a braided version BV of Thompson's group V. In this paper, we discuss some properties of BV that might make the group interesting for group

The Sigma Invariants of Thompson's Group F

Thompson's group F is the group of all increasing dyadic piecewise linear homeomorphisms of the closed unit interval. We compute Sigma^m(F) and Sigma^m(F;Z), the homotopical and homological