Many interesting geometric structures on manifolds can be interpreted as structures locally modelled on homogeneous spaces. Given a homogeneous space (X,G) and a manifold M , there is a deformation space of structures on M locally modelled on the geometry of X invariant under G. Such a geometric structure on a manifold M determines a representation (unique up to inner automorphism) of the funda...

We discuss a new method for gauge symmetry breaking in theories with one extra dimension compactified on the orbifold S1/Z2. If we assume that fields and their derivatives can jump at the orbifold fixed points, we can implement a generalized Scherk-Schwarz mechanism that breaks the gauge symmetry. We show that our model with discontinuous fields is equivalent to another with continuous but non ...

We consider normal covers of CP with abelian deck group, branched over at most four points. Families of such covers yield arithmetic Teichmüller curves, whose period mapping may be described geometrically in terms of Schwarz triangle mappings. These Teichmüller curves are generated by abelian square-tiled surfaces. We compute all individual Lyapunov exponents for abelian squaretiled surfaces, a...