Constructing the maximal monoids in the semigroups , and
Correction to "Two Generator Fuchsian Groups of Genus One".
Counting crystallographic groups in low dimensions.
Counting immersed surfaces in hyperbolic 3-manifolds.
Cross ratios, Anosov representations and the energy functional on Teichmüller space
We study two classes of linear representations of a surface group: Hitchin and maximal symplectic representations. We relate them to cross ratios and thus deduce that they are displacing which means that their translation lengths are roughly controlled by the translations lengths on the Cayley graph. As a consequence, we show that the mapping class group acts properly on the space of representations and that the energy functional associated to such a representation is proper. This implies the existence...
Cross ratios, surface groups, and diffeomorphisms of the circle
This article relates representations of surface groups to cross ratios. We first identify a connected component of the space of representations into PSL(n,ℝ) – known as the n-Hitchin component– to a subset of the set of cross ratios on the boundary at infinity of the group. Similarly, we study some representations into associated to cross ratios and exhibit a “character variety” of these representations. We show that this character variety contains alln-Hitchin components as well as the set of...
Crystallographic actions on Lie groups and post-Lie algebra structures
This survey on crystallographic groups, geometric structures on Lie groups and associated algebraic structures is based on a lecture given in the Ostrava research seminar in .
Cyclic parabolic quasiconformal groups that are not quasiconformal conjugates of Möbius groups.
Cyclic projective planes and Wada dessins.