Divergence functions of Thompson groups

2018 ◽  
Vol 201 (1) ◽  
pp. 227-242
Author(s):  
Gili Golan ◽  
Mark Sapir
Keyword(s):  
Thompson Groups

scholarly journals The isomorphism problem for Higman–Thompson groups

2011 ◽  
Vol 344 (1) ◽  
pp. 172-183 ◽  
Author(s):  
E. Pardo
Keyword(s):  
Isomorphism Problem ◽  
Thompson Groups

scholarly journals Higher dimensional generalizations of the Thompson groups

2020 ◽  
Vol 369 ◽  
pp. 107191
Author(s):  
Mark V. Lawson ◽  
Alina Vdovina
Keyword(s):  
Thompson Groups ◽  
Higher Dimensional

scholarly journals On the Haagerup and Kazhdan properties of R. Thompson’s groups

2019 ◽  
Vol 22 (5) ◽  
pp. 795-807 ◽  
Author(s):  
Arnaud Brothier ◽  
Vaughan F. R. Jones
Keyword(s):  
Commutator Subgroup ◽  
Invariant Vector ◽  
Haagerup Property ◽  
Thompson Groups ◽  
Thompson's Groups ◽  
Intermediate Subgroup ◽  
Regular Representations ◽  
Left Regular ◽  
Invariant Vectors ◽  
Property T

Abstract A machinery developed by the second author produces a rich family of unitary representations of the Thompson groups F, T and V. We use it to give direct proofs of two previously known results. First, we exhibit a unitary representation of V that has an almost invariant vector but no nonzero {[F,F]} -invariant vectors reproving and extending Reznikoff’s result that any intermediate subgroup between the commutator subgroup of F and V does not have Kazhdan’s property (T) (though Reznikoff proved it for subgroups of T). Second, we construct a one parameter family interpolating between the trivial and the left regular representations of V. We exhibit a net of coefficients for those representations which vanish at infinity on T and converge to 1 thus reproving that T has the Haagerup property after Farley who further proved that V has this property.

scholarly journals The homology of the Higman–Thompson groups

2019 ◽  
Vol 216 (2) ◽  
pp. 445-518 ◽  
Author(s):  
Markus Szymik ◽  
Nathalie Wahl
Keyword(s):  
Thompson Groups

scholarly journals On Jones’ subgroup of R. Thompson’s group T

2018 ◽  
Vol 28 (05) ◽  
pp. 877-903
Author(s):  
Jordan Nikkel ◽  
Yunxiang Ren
Keyword(s):  
Unitary Representation ◽  
Unitary Representations ◽  
Thompson Groups ◽  
Diagram Groups ◽  
Thompson’S Group ◽  
Planar Algebra ◽  
Thompson Group

Jones introduced unitary representations for the Thompson groups [Formula: see text] and [Formula: see text] from a given subfactor planar algebra. Some interesting subgroups arise as the stabilizer of certain vector, in particular the Jones subgroups [Formula: see text] and [Formula: see text]. Golan and Sapir studied [Formula: see text] and identified it as a copy of the Thompson group [Formula: see text]. In this paper, we completely describe [Formula: see text] and show that [Formula: see text] coincides with its commensurator in [Formula: see text], implying that the corresponding unitary representation is irreducible. We also generalize the notion of the Stallings 2-core for diagram groups to [Formula: see text], showing that [Formula: see text] and [Formula: see text] are not isomorphic, but as annular diagram groups they have very similar presentations.

scholarly journals Monoid generalizations of the Richard Thompson groups

2009 ◽  
Vol 213 (2) ◽  
pp. 264-278 ◽  
Author(s):  
Jean-Camille Birget
Keyword(s):  
Thompson Groups

Rb/Sr geochronology in the Thompson belt, Manitoba: implications for Aphebian crustal development and metallogenesis

1981 ◽  
Vol 18 (5) ◽  
pp. 932-943 ◽  
Author(s):  
C. Brooks ◽  
P. Theyer
Keyword(s):  
Broad Band ◽  
Early Period ◽  
Growth Trajectories ◽  
Isotopic Data ◽  
Depositional History ◽  
Sedimentary Sequences ◽  
Thompson Groups ◽  
Facies Metamorphism ◽  
History Of

The supracrustal metasediments of the Thompson belt (Pipe and Thompson Groups) show pronounced differences in Rb/Sr age (1855–1685 and 1665–1575 Ma, respectively) and initial Sr ratio (0.7096–0.7166 and 0.7203–0.7233). However, they have similar Rb/Sr ratios (0.8–1.2), and the age and isotopic differences are attributed to differing degrees of postdepositional, metamorphic reworking. The Sr-growth trajectories of these metasediments define a broad band on the evolution diagram and indicate a probable (maximum?) age of deposition of ca. 2.0 ± 0.1 Ga. Furthermore, the role of Archean detritus in the depositional history of these sediments is quite limited, based on isotopic data for the basement gneisses and adjoining granulites of the Pikwitonei region.Comparison of these data with those for metagraywackes of the adjacent Kisseynew gneisses (average [Formula: see text]) indicates that there were fundamental differences between the marine environments within which the two Aphebian sedimentary sequences were deposited. The high Rb/Sr in the Thompson belt metasediments is interpreted to reflect a relatively "long" equilibration of authigenic clays with circulating seawater (open ocean?) whereas the lower Rb/Sr of the Kisseynew metasediments reflects rapid sedimentation in an eugeosynclinal environment dominated by juvenile Aphebian material.Combined K/Ar and Rb/Sr ages suggest that the metamorphic reworking of the Thompson belt metasediments had three phases, an early period of folding ([Formula: see text]), followed by cross-folding and amphibolite facies metamorphism corresponding to the main pulse of the Hudsonian Orogeny ([Formula: see text]), and finally, late-stage shearing, faulting, and retrograde metamorphism (1625–1550 Ma). Mafic to ultramafic magmatism and associated nickel mineralization are confined to the interval between the deposition of the Thompson belt supracrustals and the first phase of Hudsonian deformation (i.e., ca. 2.1–1.8 Ga).

GROUPS WITH INDEXED CO-WORD PROBLEM

2006 ◽  
Vol 16 (05) ◽  
pp. 985-1014 ◽  
Author(s):  
DEREK F. HOLT ◽  
CLAAS E. RÖVER
Keyword(s):  
Dynamical Systems ◽  
Large Class ◽  
Word Problem ◽  
Word Problems ◽  
Automorphism Groups ◽  
Finite Automata ◽  
Restricted Class ◽  
Closure Properties ◽  
Free Products ◽  
Thompson Groups

We investigate co-indexed groups, that is groups whose co-word problem (all words defining nontrivial elements) is an indexed language. We show that all Higman–Thompson groups and a large class of tree automorphism groups defined by finite automata are co-indexed groups. The latter class is closely related to dynamical systems and includes the Grigorchuk 2-group and the Gupta–Sidki 3-group. The co-word problems of all these examples are in fact accepted by nested stack automata with certain additional properties, and we establish various closure properties of this restricted class of co-indexed groups, including closure under free products.

scholarly journals On normal subgroups of the braided Thompson groups

2018 ◽  
Vol 12 (1) ◽  
pp. 65-92 ◽  
Author(s):  
Matthew Zaremsky
Keyword(s):  
Normal Subgroups ◽  
Thompson Groups
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