All Questions
7 questions
1
vote
1
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161
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Divergence functions in hyperbolic groups
Gromov hyperbolicity has many characterizations, one of them being the existence of a super-linear divergence function, see definition below.
We note that in $\mathbb{R}^2$ there is no divergence ...
- 143
5
votes
1
answer
242
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Cancellation of elements in the Gromov boundary of a free group
Let $A$ be a finite set of free generators and their inverses and $F$ the free group generated by elements in $A$ (some call $A$ the alphabet of $F$). For each $g\in F$, use $\vert\,g\,\vert$ to ...
- 307
7
votes
1
answer
458
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A criterion for loxodromicity in Gromov-hyperbolic spaces
Recall that an isometry of a Gromov-hyperbolic space $X$ is called loxodromic if it has exactly two fixed points on the Gromov boundary $\partial X$, one being "attracting" and the other &...
- 3,399
7
votes
1
answer
372
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Thickness and hierarchical hyperbolicity
Thick metric spaces were introduced by Behrstock, Drutu and Mosher, see here. Hierarchically hyperbolic spaces were introduced by Behrstock, Hagen and Sisto, see here.
I've heard that it is open ...
- 2,090
10
votes
1
answer
737
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Parabolic subgroups of relatively hyperbolic and CAT(0) groups
Let $G$ be a finitely generated group. We say that $G$ is CAT(0) if it acts properly and co-compactly by isometries on a CAT(0) space.
We say it is hyperbolic relative to a collection $\Omega$ of ...
- 2,090
7
votes
1
answer
505
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Rational stable translation length
Let $G$ be a finitely generated group and $S$ a finite generating set and consider the word metric associated to $S$.
If $g\in G$, define its stable translation length as $l(g)=\lim_n \frac{d(e,g^n)}{...
- 2,090
2
votes
2
answers
464
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Combination theorems for discrete subgroups of isometry groups
Maskit's combination theorem says: if $M=M_1\cup_\Sigma M_2$ is a union of hyperbolic 3-manifolds $M_1=\Gamma_1\backslash H^3, M_2=\Gamma_2\backslash H^3$ along a surface $\Sigma$, and if the limit ...
- 10.4k