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Action of the Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups in genus zero

Benjamin Collas (2012)

Journal de Théorie des Nombres de Bordeaux

In this paper we establish the action of the Grothendieck-Teichmüller group G T ^ on the prime order torsion elements of the profinite fundamental group π 1 g e o m ( 0 , [ n ] ) . As an intermediate result, we prove that the conjugacy classes of prime order torsion of π ^ 1 ( 0 , [ n ] ) are exactly the discrete prime order ones of the π 1 ( 0 , [ n ] ) .

Genus 3 normal coverings of the Riemann sphere branched over 4 points.

Yolanda Fuertes, Manfred Streit (2006)

Revista Matemática Iberoamericana

In this paper we study the 5 families of genus 3 compact Riemann surfaces which are normal coverings of the Riemann sphere branched over 4 points from very different aspects: their moduli spaces, the uniform Belyi functions that factorize through the quotient by the automorphism groups and the Weierstrass points of the non hyperelliptic families.

Hodge-gaussian maps

Elisabetta Colombo, Gian Pietro Pirola, Alfonso Tortora (2001)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Invariants of bi-Lipschitz equivalence of real analytic functions

Jean-Pierre Henry, Adam Parusiński (2004)

Banach Center Publications

We construct an invariant of the bi-Lipschitz equivalence of analytic function germs (ℝⁿ,0) → (ℝ,0) that varies continuously in many analytic families. This shows that the bi-Lipschitz equivalence of analytic function germs admits continuous moduli. For a germ f the invariant is given in terms of the leading coefficients of the asymptotic expansions of f along the sets where the size of |x| |grad f(x)| is comparable to the size of |f(x)|.

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