Generators of split extensions of Abelian groups by cyclic groups

Let $G \simeq M \rtimes C$ be an $n$-generator group with $M$ Abelian and $C$ cyclic. We study the Nielsen equivalence classes and T-systems of generating $n$-tuples of $G$. The subgroup $M$ can be turned into a finitely generated faithful module over a suitable quotient $R$ of the integral group ring of $C$. When $C$ is infinite, we show that the Nielsen equivalence classes of the generating $n$-tuples of $G$ correspond bijectively to the orbits of unimodular rows in $M^{n -1}$ under the action of a subgroup of $GL_{n - 1}(R)$. Making no assumption on the cardinality of $C$, we exhibit a complete invariant of Nielsen equivalence in the case $M \simeq R$. As an application, we classify Nielsen equivalence classes and T-systems of soluble Baumslag-Solitar groups, lamplighter groups and split metacyclic groups.Comment: 36 pages, The former Theorem F.ii has been retracted because the proof was wrong and couldn't be repaired. To appear in Groups, Geometry and Dynamic

Limits of Baumslag-Solitar groups and dimension estimates in the space of marked groups

We prove that the limits of Baumslag-Solitar groups which we previously studied are non-linear hopfian C*-simple groups with infinitely many twisted conjugacy classes. We exhibit infinite presentations for these groups, classify them up to group isomorphism, describe their automorphisms and discuss the word and conjugacy problems. Finally, we prove that the set of these groups has non-zero Hausforff dimension in the space of marked groups on two generators.Comment: 30 pages, no figures, englis

Evidence for global runoff increase related to climate warming

Ongoing global climatic change initiated by the anthropogenic release of carbon dioxide is a matter of intense debate. We focus both on the impact of these climatic changes on the global hydrological cycle and on the amplitude of the increase of global and continental runoff over the last century, in relation to measured temperature increases. In this contribution, we propose an original statistical wavelet-based method for the reconstruction of the monthly discharges of worldwide largest rivers. This method provides a data-based approximation of the evolution of the annual continental and global runoffs over the last century. A consistent correlation is highlighted between global annual temperature and runoff, suggesting a 4% global runoff increase by 1 C global temperature rise. However, this global trend should be qualified at the regional scale where both increasing and decreasing trends are identified. North America runoffs appear to be the most sensitive to the recent climatic changes. Finally, this contribution provides the first experimental data-based evidence demonstrating the link between the global warming and the intensification of the global hydrological cycle. This corresponds to more intense evaporation over oceans coupled to continental precipitation increase or continental evaporation decrease. This process finally leads to an increase of the global continental runoff

Reply to comment of Legates et al.

In the previous comment, Legates et al. express concern about the statistical reliability of the positive runoff–temperature relationship presented by Labat et al. We are grateful for this opportunity to respond to these concerns. As Legates et al. correctly points out, the effect of temperature on runoff is a complex relationship, which involves precipitation, evaporation, anthropomorphic affects, among others. As such, the effect of increased temperature on runoff is strongly dependent on the identity of the watershed of interest. For example, a watershed located in a glaciated region, such as Iceland, exhibits a strong positive correlation between runoff and temperature, whereas a watershed located in a arid climate, such as the Sahara desert, exhibits a negative correlation; often there is no run off at all during the summer months in such watersheds