A. Akhmedov

activity

20092026

most citedGirth Alternative for Subgroups of PL_o(I)

4 citations · 14 across the 27 of their papers we have counts for

collaborators

Showing 2015Show all

5 papers · 1 filter

math.GR2015

Non-bi-orderability of $6_{2}$ and $7_{6}$

Azer Akhmedov, Cody Martin

We prove that the knot groups of $6_{2}$ and $7_{6}$ are not bi-orderable. These are the only two knot groups up to 7 crossings whose bi-orderability was not known. Our method applies…

math.GR2015

Finiteness of the topological rank of diffeomorphism groups

Azer Akhmedov

For a compact smooth manifold $M$ (with boundary) we prove that the topological rank of the diffeomorphism group Diff $_{0}^{k} (M)$ is finite for all $k \geq 1$ . This extends a result fr…

math.GR2015

Existence and genericity of finite topological generating sets for homeomorphism groups

Azer Akhmedov, Michael P. Cohen

We show that the topological groups $D i f f_{+}^{1} (I)$ and $D i f f_{+}^{1} (S^{1})$ of orientation-preserving $C^{1}$ -diffeomorphisms of the interval and the circle, respectively,…

math.GR2015

On groups of diffeomorphisms of the interval with finitely many fixed points

Azer Akhmedov

In [13], it is proved that any subgroup of $Diff_{+}^{ω} (I)$ (the group of orientation preserving analytic diffeomorphisms of the interval) is either metaabelian or does n…

math.GR2015

On groups of homeomorphisms of the interval with finitely many fixed points

Azer Akhmedov

We strengthen the results of \cite{A1}, consequently, we improve the claims of \cite{A2} obtaining the best possible results. Namely, we prove that if a subgroup $Γ$ of $\mathrm{Di…

Non-bi-orderability of 62​ and 76​

Finiteness of the topological rank of diffeomorphism groups

Existence and genericity of finite topological generating sets for homeomorphism groups

On groups of diffeomorphisms of the interval with finitely many fixed points

On groups of homeomorphisms of the interval with finitely many fixed points

Non-bi-orderability of $6_{2}$ and $7_{6}$