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Cannon-Thurston Maps, i-bounded Geometry and a Theorem of McMullen

Mahan Mj (2009/2010)

Séminaire de théorie spectrale et géométrie

The notion of i-bounded geometry generalises simultaneously bounded geometry and the geometry of punctured torus Kleinian groups. We show that the limit set of a surface Kleinian group of i-bounded geometry is locally connected by constructing a natural Cannon-Thurston map.

Characteres and Galois invariants of regular dessins.

Manfred Streit, Jürgen Wolfart (2000)

Revista Matemática Complutense

We describe a new invariant for the action of the absolute Galois groups on the set of Grothendieck dessins. It uses the fact that the automorphism groups of regular dessins are isomorphic to automorphism groups of the corresponding Riemman surfaces and define linear represenatations of the space of holomorphic differentials. The characters of these representations give more precise information about the action of the Galois group than all previously known invariants, as it is shown by a series...

Conformal actions with prescribed periods on Riemann surfaces

G. Gromadzki, W. Marzantowicz (2011)

Fundamenta Mathematicae

It is a natural question what is the set of minimal periods of a holomorphic maps on a Riemann surface of negative Euler characteristic. Sierakowski studied ordinary holomorphic periods on classical Riemann surfaces. Here we study orientation reversing automorphisms acting on classical Riemann surfaces, and also automorphisms of non-orientable unbordered Klein surfaces to which, following Singerman, we shall refer to as non-orientable Riemann surfaces. We get a complete set of conditions for the...

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