scholarly journals The type and stable type of the boundary of a Gromov hyperbolic group

2013 ◽  
Vol 172 (1) ◽  
pp. 363-386 ◽  
Author(s):  
Lewis Bowen
Keyword(s):  
Hyperbolic Group ◽  
Stable Type ◽  
Gromov Hyperbolic ◽  
Gromov Hyperbolic Group

scholarly journals FREELY INDECOMPOSABLE GROUPS ACTING ON HYPERBOLIC SPACES

2004 ◽  
Vol 14 (02) ◽  
pp. 115-171 ◽  
Author(s):  
ILYA KAPOVICH ◽  
RICHARD WEIDMANN
Keyword(s):  
Hyperbolic Group ◽  
Conjugacy Classes ◽  
Hyperbolic Spaces ◽  
Gromov Hyperbolic ◽  
Torsion Free

We obtain a number of finiteness results for groups acting on Gromov-hyperbolic spaces. In particular we show that a torsion-free locally quasiconvex hyperbolic group has only finitely many conjugacy classes of n-generated one-ended subgroups.

scholarly journals Quantitative residual properties of Γ-limit groups

2014 ◽  
Vol 24 (02) ◽  
pp. 207-231
Author(s):  
Brent B. Solie
Keyword(s):  
Hyperbolic Group ◽  
Finitely Generated ◽  
Limit Group ◽  
Limit Groups ◽  
Residual Properties

Let Γ be a fixed hyperbolic group. The Γ-limit groups of Sela are exactly the finitely generated, fully residually Γ groups. We introduce a new invariant of Γ-limit groups called Γ-discriminating complexity. We further show that the Γ-discriminating complexity of any Γ-limit group is asymptotically dominated by a polynomial.

Mathematical Properties of Gromov Hyperbolic Graphs

2010 ◽  
Author(s):  
Sergio Bermudo ◽  
José M. Rodríguez ◽  
José M. Sigarreta ◽  
Jean-Marie Vilaire ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Mathematical Properties ◽  
Gromov Hyperbolic ◽  
Hyperbolic Graphs

scholarly journals Equations in the Q-completion of a torsion-free hyperbolic group

1999 ◽  
Vol 351 (7) ◽  
pp. 2961-2978
Author(s):  
O. Kharlampovich ◽  
E. Lioutikova ◽  
A. Myasnikov
Keyword(s):  
Hyperbolic Group ◽  
Torsion Free

scholarly journals The Baum-Connes conjecture, noncommutative Poincaré duality, and the boundary of the free group

2003 ◽  
Vol 2003 (38) ◽  
pp. 2425-2445 ◽  
Author(s):  
Heath Emerson
Keyword(s):  
Free Group ◽  
Homology Class ◽  
Hyperbolic Group ◽  
Cross Product ◽  
Direct Connection ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Duality Map ◽  
The Cross ◽  
Gromov Boundary

For every hyperbolic groupΓwith Gromov boundary∂Γ, one can form the cross productC∗-algebraC(∂Γ)⋊Γ. For each such algebra, we construct a canonicalK-homology class. This class induces a Poincaré duality mapK∗(C(∂Γ)⋊Γ)→K∗+1(C(∂Γ)⋊Γ). We show that this map is an isomorphism in the case ofΓ=𝔽2, the free group on two generators. We point out a direct connection between our constructions and the Baum-Connes conjecture and eventually use the latter to deduce our result.

scholarly journals DECIDABILITY AND COMPLEXITY IN AUTOMATIC MONOIDS

2005 ◽  
Vol 16 (04) ◽  
pp. 707-722 ◽  
Author(s):  
MARKUS LOHREY
Keyword(s):  
Cayley Graph ◽  
Word Problem ◽  
Hyperbolic Group ◽  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Decidability And Complexity

Several complexity and decidability results for automatic monoids are shown: (i) there exists an automatic monoid with a P-complete word problem, (ii) there exists an automatic monoid such that the first-order theory of the corresponding Cayley-graph is not elementary decidable, and (iii) there exists an automatic monoid such that reachability in the corresponding Cayley-graph is undecidable. Moreover, it is shown that for every hyperbolic group the word problem belongs to LOGCFL, which improves a result of Cai [8].

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