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Euler characteristics of moduli spaces of curves

Gilberto Bini, John Harer (2011)

Journal of the European Mathematical Society

Let M g n be the moduli space of n -pointed Riemann surfaces of genus g . Denote by M g n ¯ the Deligne-Mumford compactification of M g n . In the present paper, we calculate the orbifold and the ordinary Euler characteristic of M g n ¯ for any g and n such that n > 2 - 2 g .

Exotic Deformations of Calabi-Yau Manifolds

Paolo de Bartolomeis, Adriano Tomassini (2013)

Annales de l’institut Fourier

We introduce Quantum Inner State manifolds (QIS manifolds) as (compact) 2 n -dimensional symplectic manifolds ( M , κ ) endowed with a κ -tamed almost complex structure J and with a nowhere vanishing and normalized section ϵ of the bundle Λ J n , 0 ( M ) satisfying the condition ¯ J ϵ = 0 .We study the moduli space 𝔐 of QIS deformations of a given Calabi-Yau manifold, computing its tangent space and showing that 𝔐 is non obstructed. Finally, we present several examples of QIS manifolds.

Exponential mixing for the Teichmüller flow

Artur Avila, Sébastien Gouëzel, Jean-Christophe Yoccoz (2006)

Publications Mathématiques de l'IHÉS

We study the dynamics of the Teichmüller flow in the moduli space of abelian differentials (and more generally, its restriction to any connected component of a stratum). We show that the (Masur-Veech) absolutely continuous invariant probability measure is exponentially mixing for the class of Hölder observables. A geometric consequence is that the S L ( 2 , ) action in the moduli space has a spectral gap.

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