Deciding whether a mapping torus is of full rank

The mapping torus induced by an automorphism $\phi$ of the free abelian group $\mathbb{Z}^n$ is a semi-direct product $G=\mathbb{Z}^n\rtimes_\phi \mathbb{Z}$. We show that whether the rank of $G$ is equal to $n+1$ is decidable. As a corollary, the rank of $\mathbb{Z}^3\rtimes_\phi \mathbb{Z}$ is decidable

A note on the free degrees of homeomorphisms on genus 2 orientable compact surfaces

AbstractFor a compact surface F, the free degree fr(F) of homeomorphisms on F is defined as the maximum of least periods among all periodic points of self-homeomorphisms on F. We show that maxbfr(F2,b)=12

Supersolvable closures of finitely generated subgroups of the free group

We prove the pro-supersolvable closure of a finitely generated subgroup of the free group is finitely generated. It extends similar results for pro-$p$ closures proved by Ribes-Zalesskii and pro-Nilpotent closures proved by Margolis-Sapir-Weil

Self-mapping degrees of torus bundles and torus semi-bundles

Each closed oriented 3-manifold M is naturally associated with a set of integers D(M), the degrees of all self-maps on M. D(M) is determined for each torus bundle and semi-bundle M. The structure of torus semi-bundle is studied in detail. The paper is a part of a project to determine D(M) for all 3-manifolds in Thurston's picture.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000277823900008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701MathematicsSCI(E)6ARTICLE1131-1554

Fixed subgroups are compressed in surface groups

For a compact surface $\Sigma$ (orientable or not, and with boundary or not) we show that the fixed subgroup, $\operatorname{Fix} B$, of any family $B$ of endomorphisms of $\pi_1(\Sigma)$ is compressed in $\pi_1(\Sigma)$ i.e., $\operatorname{rk}((\operatorname{Fix} B)\cap H)\leq \operatorname{rk}(H)$ for any subgroup $\operatorname{Fix} B \leq H \leq \pi_1(\Sigma)$. On the way, we give a partial positive solution to the inertia conjecture, both for free and for surface groups. We also investigate direct products, $G$, of finitely many free and surface groups, and give a characterization of when $G$ satisfies that $\operatorname{rk}(\operatorname{Fix} \phi) \leq \operatorname{rk}(G)$ for every $\phi \in Aut(G)$

Fixed subgroups in direct products of surface groups of Euclidean type

We give an explicit characterization of which direct products G of surface groups of Euclidean type satisfy that the fixed subgroup of any automorphism (or endomorphism) of G is compressed, and of which is it always inert.Peer ReviewedPostprint (author's final draft

Self-mapping degrees of 3-manifolds

For each closed oriented 3-manifold M in Thurston's picture, the set of degrees of self-maps on M is given.MathematicsSCI(E)2ARTICLE1247-2694