13 research outputs found
Fixed subgroups are compressed in surface groups
For a compact surface (orientable or not, and with boundary or not)
we show that the fixed subgroup, , of any family of
endomorphisms of is compressed in i.e.,
for
any subgroup . 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, , of finitely many
free and surface groups, and give a characterization of when satisfies that
for
every
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
Explicit bounds for fixed subgroups of endomorphisms of free products
For an automorphism of a free group of rank , Bestvina and
Handel showed that the rank of the fixed subgroup is not greater
than (the so-called Scott conjecture). Soon after Bestvina and Handel's
announcement, their result was generalized by many authors in various
directions. In this paper, we are interested in the fixed subgroups of
endomorphisms of free products, focusing on explicit bounds for their ranks.Comment: 12 page
The Equalizer Conjecture for the free group of rank two
Funding: This research was supported by Engineering and Physical Sciences Research Council (EPSRC) grant EP/R035814/1.The equalizer of a set of homomorphisms S : F(a,b) → F(Δ) has rank at most two if S contains an injective map and is not finitely generated otherwise. This proves a strong form of Stallings’ Equalizer Conjecture for the free group of rank two. Results are also obtained for pairs of homomorphisms g,h : F(Σ) → F(Δ) when the images are inert in, or retracts of, F(Δ).Publisher PDFPeer reviewe
Publicacions científiques de l'Escola Politècnica Superior d'Enginyeria de Manresa (EPSEM) curs 2014-2015
Aquest estudi ha estat elaborat per la Biblioteca del Campus Universitari de Manresa amb l'objectiu de proveir dades per la memòria del curs 2014-2015 de l'Escola Politècnica Superior d'Enginyeria de Manresa. Recull les publicacions dels investigadors del centre durant el curs, extretes de Futur.upc.edu i analitzades a Scopus.Postprint (published version
Degrees of compression and inertia for free-abelian times free groups
© 2020. ElsevierWe introduce the concepts of degree of inertia, diG(H), and degree of compression,dcG(H), of a finitely generated subgroupHof a given groupG. For the case of direct productsof free-abelian and free groups, we compute the degree of compression and give an upper boundfor the degree of inertia. Imposing some technical assumptions to the supremum involved in thedefinition of degree of inertia, we introduce the notion called restricted degree of inertia, di'G(H),and, again for the caseZm×Fn, we provide an explicit formula relating it to the restricted degreeof inertia of its projection to the free part, di'Fn(Hp).Both authors are partially supported by the Spanish Agencia Estatalde Investigación, through grant MTM2017-82740-P (AEI/ FEDER, UE), and also by the “María de Maeztu” Programme for Units of Excellence in R&D (MDM-2014-0445)Peer ReviewedPostprint (author's final draft