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Results tagged with geometric-group-theory
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user 6503
Large scale properties of groups; growth functions; Dehn functions; small cancellation properties; hyperbolicity and CAT(0); actions and representations; combinatorial group theory; presentations
15
votes
Classes of groups with polynomial time isomorphism problem
A two-generator, one-relator group with torsion is a group with presentation of the form $\langle a, b\mid R^n\rangle$, $R\in F(a, b)$ and $n>1$. Their isomorphism problem is decidable in quadratic ti …
- 2,821
8
votes
0
answers
273
views
Subgroups of torsion-free hyperbolic groups versus subgroups of hyperbolic groups
Let $\mathcal{S}$ be the class of finitely presented torsion-free groups which occur as the subgroup of some hyperbolic group (so for every $G\in \mathcal{S}$ there exists a hyperbolic group $H$ such …
- 2,821
4
votes
1
answer
427
views
When is a generalised Baumslag-Solitar group linear?
$\DeclareMathOperator\BS{BS}$The linearity of the Baumslag-Solitar groups $\BS(m, n)=\langle a, t\mid t^{-1}a^mt=a^n\rangle$ is completely understood, and it may be phrased as: $\BS(m, n)$ is linear i …
- 2,821
4
votes
Groups acting non-properly cocompactly on hyperbolic spaces
Bass-Serre theory is the classical theory of groups acting on trees. Trees are hyperbolic, so this theory fits nicely into the context of this question.
Standard examples of groups acting on trees co- …
- 2,821
2
votes
$C'(\lambda)$ small cancellation for $\lambda < \frac{1}{6}$
Greendlinger's Lemma is about the geometry of disk diagrams. If we instead consider annular diagrams, the assumption that $\lambda<1/8$ gives an improved structural result.
Annular diagrams encode the …
- 2,821