Metric properties of Baumslag-Solitar groups

© 2015 World Scientific Publishing Company. We compute estimates for the word metric of Baumslag-Solitar groups in terms of the Britton's lemma normal form. As a corollary, we find lower bounds for the growth rate for the groups BS(p, q) with 1 < p ≤ q

Estudi bibliomètric any 2016. EETAC

El present document recull les publicacions indexades a la base de dades Scopus durant el període comprès entre el mesos de gener a desembre de l’any 2016, escrits per autors pertanyents a l’EETAC. Es presenten les dades recollides segons la font on s’ha publicat, els autors que han publicat, i el tipus de document publicat. S’hi inclou un annex amb la llista de totes les referències bibliogràfiques publicades.Postprint (author's final draft

Estudi bibliomètric any 2015. EETAC

El present document recull les publicacions indexades a la base de dades Scopus durant el període comprès entre el mesos de gener a desembre de l’any 2015, escrits per autors pertanyents a l’EETAC. Es presenten les dades recollides segons la font on s’ha publicat, els autors que han publicat, i el tipus de document publicat. S’hi inclou un annex amb la llista de totes les referències bibliogràfiques publicades.Postprint (published version

C-graph automatic groups

We generalize the notion of a graph automatic group introduced by Kharlampovich, Khoussainov and Miasnikov by replacing the regular languages in their definition with more powerful language classes. For a fixed language class C, we call the resulting groups C-graph automatic. We prove that the class of C-graph automatic groups is closed under change of generating set, direct and free product for certain classes C. We show that for quasi-realtime counter-graph automatic groups where normal forms have length that is linear in the geodesic length, there is an algorithm to compute normal forms (and therefore solve the word problem) in polynomial time. The class of quasi-realtime counter-graph automatic groups includes all Baumslag-Solitar groups, and the free group of countably infinite rank. Context-sensitive-graph automatic groups are shown to be a very large class, which encompasses, for example, groups with unsolvable conjugacy problem, the Grigorchuk group, and Thompson's groups F, T and V. © 2014 Elsevier Inc

Conjugation Curvature in Solvable Baumslag-Solitar Groups

For an element in $BS(1,n) = \langle t,a | tat^{-1} = a^n \rangle$ written in the normal form $t^{-u}a^vt^w$ with $u,w \geq 0$ and $v \in \mathbb{Z}$, we exhibit a geodesic word representing the element and give a formula for its word length with respect to the generating set $\{t,a\}$. Using this word length formula, we prove that there are sets of elements of positive density of positive, negative and zero conjugation curvature, as defined by Bar Natan, Duchin and Kropholler.Comment: 50 pages, 3 figure

Eigenvalue gaps for hyperbolic groups and semigroups

Given a locally constant linear cocycle over a subshift of finite type, we show that the existence of a uniform gap between the i-th and (i+1)-th Lyapunov exponents for all invariant measures implies the existence of a dominated splitting of index i. We establish a similar result for sofic subshifts coming from word hyperbolic groups, in relation with Anosov representations of such groups. We discuss the case of finitely generated semigroups, and propose a notion of Anosov representation in this setting.Comment: 37 page

Groups defined by language theoretic classes

In this thesis we shall study classes of groups defined by formal languages. Our first main topic is the class of groups defined by having an ET0L co-word problem; i.e., the class of co-ET0L groups. We show this class is closed under taking direct products and standard restricted wreath products with virtually free top groups. We also show the class is closed under passing to finite index overgroups and finitely generated subgroups. Further, we show that this class contains the free product Zn * Zm as well as Zn * G for any virtually free group G. The second topic that we consider is a new class of groups that we introduce called epiregular groups. We show that this class contains all automatic groups and the Baumslag-Solitar group BS(1,2). Further we show that the class of epiregular groups is closed under taking graph products, and passing to finite index overgroups