Examples of retracts in a free group that are not the fixed subgroup of any group of automorphisms

Let F be a free group of rank at least three. We show that some retracts of F previously studied by Martino-Ventura are not equal to the fixed subgroup of any group of automorphisms of F. This shows that, in F, there exist subgroups that are equal to the fixed subgroup of some set of endomorphisms but are not equal to the fixed subgroup of any set of automorphisms. Moreover, we determine the Galois monoids of these retracts, where, by the Galois monoid of a subgroup H of F, we mean the monoid consisting of all endomorphisms of F that fix H.

On Hyperbolic once-punctured-torus bundles II. Fractal tessellations of the plane

We describe fractal tessellations of the complex plane that arise naturally from Cannon-Thurston maps associated to complete, hyperbolic, once-punctured-torus bundles. We determine the symmetry groups of these tessellations.

The Patterson-Sullivan embedding and minimal volume entropy for outer space

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The missing link in key sectors analysis

In general terms key sectors analysis aims at identifying the role, or impact, that the existence of a productive sector has in the economy. Quite a few measures, indicators and methodologies of varied complexity have been proposed in the literature, from multiplier sums to extraction methods, but not without debate about their properties and their information content. All of them, to our knowledge, focus exclusively on the interdependence effects that result from the input-output structure of the economy. By so doing the simple input-output approach misses critical links beyond the interindustry ones. A productive sector’s role is that of producing but also that of generating and distributing income among primary factors as a result of production. Thus when measuring a sector’s role, the income generating process cannot and should not be omitted if we want to better elucidate the sector’ economic role. A simple way to make the missing income link explicit is to use the SAM (Soci

A general construction of internal sheaves in algebraic set theory

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothen-dieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

On the intersection of free subgroups in free products of groups

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On hyperbolic once-punctured-torus bundles IV: automata for lightning curves

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¿Son nuestros repositorios lo suficientemente sólidos como para asumir mandatos institucionales?

Aquesta comunicació se centra en l'estudi de la mida, la flexibilitat i l'estabilitat dels equips que gestionen els dipòsits espanyols en l'actualitat, per tal de determinar si són prou sòlids i estables com per suportar mandats institucionals. Per això s'ha realitzat una enquesta entre els dipòsits per tal de recopilar informació sobre l'estructura dels equips professionals que els gestionen. Atès que el nivell de desenvolupament entre els dipòsits espanyols és molt diferent, l'anàlisi se centrarà inicialment en aquells que es troben més consolidats, encara que la intenció de l'estudi és assolir un nivell de cobertura el més ampli possible que eventualment pugui excedir els límits nacionals.

La Tortuga de l’Albera : proposta d’actuació per a la recuperació del seu hàbitat de nidificació

Estudi biològic de la tortuga mediterrània a la Serra de l’Albera, factors d’amenaça, creació de noves zones de posta i manteniment a llarg termini per tal d’augmentar la seva supervivència de cara a conservar i incrementar l’última població autòctona de tortuga mediterrània a la Península Ibèrica