E-polynomials of the SL(2, C)-character varieties of surface groups

We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a once-punctured surface of any genus into SL(2, C), for any possible holonomy around the puncture. We follow the geometric technique introduced in [12], based on stratifying the space of representations, and on the analysis of the behavior of the E-polynomial under fibrations.

Mackey topology on locally convex spaces and on locally quasi-convex groups. Similarities and historical remarks

A counterpart of the Mackey–Arens Theorem for the class of locally quasi-convex topological Abelian groups (LQC-groups) was initiated in Chasco et al. (Stud Math 132(3):257–284, 1999). Several authors have been interested in the problems posed there and have done clarifying contributions, although the main question of that source remains open. Some differences between the Mackey Theory for locally convex spaces and for locally quasi-convex groups, stem from the following fact: The supremum of all compatible locally quasi-convex topologies for a topological abelian group G may not coincide with the topology of uniform convergence on the weak quasi-convex compact subsets of the dual groupG∧. Thus, a substantial part of the classical Mackey–Arens Theorem cannot be generalized to LQC-groups. Furthermore, the mentioned fact gives rise to a grading in the property of “being a Mackey group”, as defined and thoroughly studied in Díaz Nieto and Martín-Peinador (Proceedings in Mathematics and Statistics 80:119–144, 2014). At present it is not known—and this is the main open question—if the supremum of all the compatible locally quasi-convex topologies on a topological group is in fact a compatible topology. In the present paper we do a sort of historical review on the Mackey Theory, and we compare it in the two settings of locally convex spaces and of locally quasi-convex groups. We point out some general questions which are still open, under the name of Problems.

Impact of the use of β-lactam antimicrobials on the emergence of Escherichia coli isolates resistant to cephalosporins under standard pig-rearing conditions

The aim of this study was to evaluate if the treatments with ceftiofur and amoxicillin are risk factors for the emergence of cephalosporin resistant (CR) E. coli in a pig farm during the rearing period. One hundred 7-day-old piglets were divided into two groups, a control (n = 50) group and a group parenterally treated with ceftiofur (n = 50). During the fattening period, both groups were subdivided in two. A second treatment with amoxicillin was administered in feed to two of the four groups, as follows: group 1 (untreated, n = 20), group 2 (treated with amoxicillin, n = 26), group 3 (treated with ceftiofur, n = 20), and group 4 (treated with ceftiofur and amoxicillin, n = 26). During treatment with ceftiofur, fecal samples were collected before treatment (day 0) and at days 2, 7, 14, 21, and 42 posttreatment, whereas with amoxicillin, the sampling was extended 73 days posttreatment. CR E. coli bacteria were selected on MacConkey agar with ceftriaxone (1 mg/liter). Pulsed-field gel electrophoresis (PFGE), MICs of 14 antimicrobials, the presence of cephalosporin resistance genes, and replicon typing of plasmids were analyzed. Both treatments generated an increase in the prevalence of CR E. coli, which was statistically significant in the treated groups. Resistance diminished after treatment. A total of 47 CR E. coli isolates were recovered during the study period; of these, 15 contained blaCTX-M-1, 10 contained blaCTX-M-14, 4 contained blaCTX-M-9, 2 contained blaCTX-M-15, and 5 contained blaSHV-12. The treatment with ceftiofur and amoxicillin was associated with the emergence of CR E. coli during the course of the treatment. However, by the time of finishing, CR E. coli bacteria were not recovered from the animals.