Displaying similar documents to “Invariants of translation surfaces”

Veech Groups of Loch Ness Monsters

Piotr Przytycki, Gabriela Schmithüsen, Ferrán Valdez (2011)

Annales de l’institut Fourier

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We classify Veech groups of tame non-compact flat surfaces. In particular we prove that all countable subgroups of G L + ( 2 , R ) avoiding the set of mappings of norm less than 1 appear as Veech groups of tame non-compact flat surfaces which are Loch Ness monsters. Conversely, a Veech group of any tame flat surface is either countable, or one of three specific types.

On ovals on Riemann surfaces.

Grzegorz Gromadzki (2000)

Revista Matemática Iberoamericana

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We prove that k (k ≥ 9) non-conjugate symmetries of a Riemann surface of genus g have at most 2g - 2 + 2(9 - k) ovals in total, where r is the smallest positive integer for which k ≤ 2. Furthermore we prove that for arbitrary k ≥ 9 this bound is sharp for infinitely many values of g.

A family of M-surfaces whose automorphism groups act transitively on the mirrors.

Adnan Melekoglu (2000)

Revista Matemática Complutense

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Let X be a compact Riemmann surface of genus g > 1. A symmetry T of X is an anticonformal involution. The fixed point set of T is a disjoint union of simple closed curves, each of which is called a mirror of T. If T fixes g +1 mirrors then it is called an M-symmetry and X is called an M-surface. If X admits an automorphism of order g + 1 which cyclically permutes the mirrors of T then we shall call X an M-surface with the M-property. In this paper we investigate those M-surfaces...

Lifting di-analytic involutions of compact Klein surfaces to extended-Schottky uniformizations

Rubén A. Hidalgo (2011)

Fundamenta Mathematicae

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Let S be a compact Klein surface together with a di-analytic involution κ: S → S. The lowest uniformizations of S are those whose deck group is an extended-Schottky group, that is, an extended Kleinian group whose orientation preserving half is a Schottky group. If S is a bordered compact Klein surface, then it is well known that κ can be lifted with respect to a suitable extended-Schottky uniformization of S. In this paper, we complete the above lifting property by proving that if S...