arXiv subjects

Daciberg Goncalves

Publications and source records attributed to Daciberg Goncalves.

4 recordsLinked to original sources

arXiv2020

Twisted conjugacy in free products

Let $ϕ:G\to G$ be an automorphism of a group which is a free-product of finitely many groups each of which is freely indecomposable and two of the factors contain proper finite index characteristic subgroups. We show that $G$ has infinitely many $ϕ$-twisted conjugacy classes. As an application, we show that if $G$ is the fundamental group of a three-manifold that is not irreducible, then $G$ has property $R_\infty$, that is, there are infinitely many $ϕ$-twisted conjugacy classes in $G$ for every automorphism $ϕ$ of $G$.

math.GR↗

arXiv2014

Twisted conjugacy in generalized Thompson groups of type F

If $ϕ$ is an automorphism of a group $G$ and $x,y\in G$, we say that $x$ and $y$ are $ϕ$-twisted conjugates if there exists an $z\in G$ such that $y=z.x.ϕ(z^{-1})$. This is an equivalence relation. If there are infinitely many $ϕ$-twisted conjugacy classes for every automorphism $ϕ$ of $G$ we say that $G$ has the $R_\infty$-property. We prove that the generalized Richard Thompson groups $F_n$ and $F(l,A,P)$ have the $R_\infty$-property.

math.GR↗

arXiv2009

Some quadratic equations in the free group of rank 2

For a given quadratic equation with any number of unknowns in any free group F, with right-hand side an arbitrary element of F, an algorithm for solving the problem of the existence of a solution was given by Culler. The problem has been studied by the authors for parametric families of quadratic equations arising from continuous maps between closed surfaces, with certain conjugation factors as the parameters running through the group F. In particular, for a one-parameter family of quadratic equations in the free group F_2 of rank 2, corresponding to maps of absolute degree 2 between closed surfaces of Euler characteristic 0, the problem of the existence of faithful solutions has been solved in terms of the value of the self-intersection index mu: F_2 --> Z[F_2] on the conjugation parameter. The present paper investigates the existence of faithful, or non-faithful, solutions of similar families of quadratic equations corresponding to maps of absolute degree 0.

math.GR↗

arXiv2007

A note on generalized equivariant homotopy groups

In this paper, we generalize the equivariant homotopy groups or equivalently the Rhodes groups. We establish a short exact sequence relating the generalized Rhodes groups and the generalized Fox homotopy groups and we introduce $Γ$-Rhodes groups, where $Γ$ admits a certain co-grouplike structure. Evaluation subgroups of $Γ$-Rhodes groups are discussed.

math.AT↗