Free group automorphisms with parabolic boundary orbits

For $N\geq 4$, we show that there exist automorphisms of the free group $F_N$ which have a parabolic orbit in $\partial F_N$. In fact, we exhibit a technology for producing infinitely many such examples

A finitely generated, locally indicable group with no faithful action by C^1 diffeomorphisms of the interval

According to Thurston's stability theorem, every group of C^1 diffeomorphisms of the closed interval is locally indicable (.e., every finitely generated subgroup factors through Z). We show that, even for finitely generated groups, the converse of this statement is not true. More precisely, we show that the semi-direct product between F_2 an Z^2, although locally indicable, does not embed into Diff_+^1 (]0,1[). (Here F_2 is any free subgroup of SL(2,Z), and its action on Z^2 is the projective one.) Moreover, we show that for every non-solvable subgroup G of SL(2,Z), the semi-direct product between G and Z^2 does not embed into Diff^1_+(S^1).Comment: 8 pages, no figur

Chercher midi à midi et quart !

International audienceMa belle-sœur Aline affirme qu'en janvier, les journées rallongent moins le matin que le soir. A-t-elle raison

Chemical Vapor Deposition of silicon nanodots on TiO2 submicronic powders in vibrated fluidized bed

Silicon nanodots have been deposited on TiO2 submicronic powders in a vibrated Fluidized Bed Chemical Vapor Deposition (FBCVD) reactor from silane SiH4. Deposition conditions involving very low deposition rates have been studied. After treatment, powders are under the form of micronic agglomerates. In the operating range tested, this agglomerates formation mainly depends on the fluidization conditions and not on the CVD parameters. The best results have been obtained for anatase TiO2 powders for which the conditions of fluidization have been the most optimized. For these anatase powders, agglomerates are porous. SEM and TEM imaging prove that silicon nanodots (8-10 nm in size) have been deposited on the surface of particles and that this deposition is uniform on the whole powders and conformal around each grain, even if not fully continuous. Raman spectroscopy shows that the TiO2 powders have been partially reduced into TiO2-x during deposition. The TiO2 stoichiometry can be recovered by annealing under air, and IR spectroscopy indicates that the deposited silicon nanodots have been at least partly oxidized into SiO2 after this annealing

Length functions of Hitchin representations

Given a Hitchin representation \rho \colon \pi_1(S) \to \PSL_n(\mathbb{R}), we construct $n$ continuous functions \ell_i^\rho \colon \mathcal \CH(S) \to \mathbb{R} defined on the space of H\"older geodesic currents \CH(S) such that, for a closed, oriented curve $\gamma$ in $S$, the $i$--th eigenvalue of the matrix \rho(\gamma)\in \PSL_n(\mathbb{R}) is of the form $\pm \mathrm{exp}\, \ell_i^\rho(\gamma)$: such functions generalize to higher rank Thurston's length function of Fuchsian re\presentations. Identities, diffe\rentiability properties of these lengths $\ell_i^\rho$, as well as applications to eigenvalue estimates, are also considered.Comment: 16 pages, 2 figures, final version to appear in Algebraic and Geometric Topolog

Commutator length of annulus diffeomorphisms

We study the group of C^{r}-diffeomorphisms of the closed annulus that are isotopic to the identity. We show that, for r different from 3, the linear space of homogeneous quasi-morphisms on this group is one dimensional. Therefore, the commutator length on this group is (stably) unbounded. In particular, this provides an example of a manifold whose diffeomorphisms group is unbounded in the sense of Burago, Ivanov and Polterovich