scholarly journals Commensurability in Artin groups of spherical type

2021 ◽  
Author(s):  
María Cumplido ◽  
Luis Paris
Keyword(s):  
Artin Groups ◽  
Spherical Type

BIRMAN'S CONJECTURE IS TRUE FOR I2(p)

2006 ◽  
Vol 15 (02) ◽  
pp. 167-177 ◽  
Author(s):  
JAMES EAST
Keyword(s):  
Group Ring ◽  
Braid Group ◽  
Integral Group Ring ◽  
Integral Group ◽  
Artin Groups ◽  
Spherical Type

In 1993, Birman conjectured that the desingularization map from the singular braid monoid to the integral group ring of the braid group determined by [Formula: see text] and [Formula: see text] is injective. The conjecture, which has recently been proven true by Paris (2004), may be generalized to all Artin groups. In this article we prove that the generalized conjecture holds for one of the infinite families of Artin groups of spherical type, namely I2(p).

scholarly journals Artin groups of spherical type up to isomorphism

2004 ◽  
Vol 281 (2) ◽  
pp. 666-678 ◽  
Author(s):  
Luis Paris
Keyword(s):  
Artin Groups ◽  
Spherical Type

scholarly journals Graphical splittings of Artin kernels

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Enrique Miguel Barquinero ◽  
Lorenzo Ruffoni ◽  
Kaidi Ye
Keyword(s):  
Free Group ◽  
Artin Group ◽  
Artin Groups ◽  
Graphs Of Groups ◽  
Underlying Graph ◽  
Block Graphs ◽  
Right Angled Artin Groups

Abstract We study Artin kernels, i.e. kernels of discrete characters of right-angled Artin groups, and we show that they decompose as graphs of groups in a way that can be explicitly computed from the underlying graph. When the underlying graph is chordal, we show that every such subgroup either surjects to an infinitely generated free group or is a generalized Baumslag–Solitar group of variable rank. In particular, for block graphs (e.g. trees), we obtain an explicit rank formula and discuss some features of the space of fibrations of the associated right-angled Artin group.

scholarly journals On parabolic subgroups of Artin–Tits groups of spherical type

2019 ◽  
Vol 352 ◽  
pp. 572-610 ◽  
Author(s):  
María Cumplido ◽  
Volker Gebhardt ◽  
Juan González-Meneses ◽  
Bert Wiest
Keyword(s):  
Parabolic Subgroups ◽  
Spherical Type

scholarly journals The BNS-invariant for some Artin groups of arbitrary circuit rank

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Kisnney Almeida
Keyword(s):  
Artin Groups

AbstractWe classify the Bieri–Neumann–Strebel invariant

On a conjecture in Artin groups

2021 ◽  
pp. 1-25
Author(s):  
Arye Juhász
Keyword(s):  
Artin Group ◽  
Two Dimensional ◽  
Artin Groups ◽  
Small Cancellation ◽  
Small Cancellation Theory ◽  
Infinite Type ◽  
Trivial Center

It is conjectured that an irreducible Artin group which is of infinite type has trivial center. The conjecture is known to be true for two-dimensional Artin groups and for a few other types of Artin groups. In this work, we show that the conjecture holds true for Artin groups which satisfy a condition stronger than being of infinite type. We use small cancellation theory of relative presentations.

Solution of the Problem of Equality and Conjugacy of Words in a Certain Class of Artin Groups

2021 ◽  
Vol 257 (6) ◽  
pp. 751-764
Author(s):  
V. N. Bezverkhnii ◽  
N. B. Bezverkhnyaya
Keyword(s):  
Artin Groups
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