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Margulis Lemma, entropy and free products

Filippo Cerocchi (2014)

Annales de l’institut Fourier

We prove a Margulis’ Lemma à la Besson-Courtois-Gallot, for manifolds whose fundamental group is a nontrivial free product A * B , without 2-torsion. Moreover, if A * B is torsion-free we give a lower bound for the homotopy systole in terms of upper bounds on the diameter and the volume-entropy. We also provide examples and counterexamples showing the optimality of our assumption. Finally we give two applications of this result: a finiteness theorem and a volume estimate for reducible manifolds.

Maslov indices on the metaplectic group M p ( n )

Maurice De Gosson (1990)

Annales de l'institut Fourier

We use the properties of M p ( n ) to construct functions μ ℓ : M p ( n ) → Z 8 associated with the elements ℓ of the lagrangian grassmannian Λ (n) which generalize the Maslov index on Mp(n) defined by J. Leray in his “Lagrangian Analysis”. We deduce from these constructions the identity between M p ( n ) and a subset of S p ( n ) × Z 8 , equipped with appropriate algebraic and topological structures.

Mass endomorphism, surgery and perturbations

Bernd Ammann, Mattias Dahl, Andreas Hermann, Emmanuel Humbert (2014)

Annales de l’institut Fourier

We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.

Maximal Hamiltonian tori for polygon spaces

Jean-Claude Hausmann, Susan Tolman (2003)

Annales de l’institut Fourier

We study the poset of Hamiltonian tori for polygon spaces. We determine some maximal elements and give examples where maximal Hamiltonian tori are not all of the same dimension.

Maximal rationally connected fibrations and movable curves

Luis E. Solá Conde, Matei Toma (2009)

Annales de l’institut Fourier

A well known result of Miyaoka asserts that a complex projective manifold is uniruled if its cotangent bundle restricted to a general complete intersection curve is not nef. Using the Harder-Narasimhan filtration of the tangent bundle, it can moreover be shown that the choice of such a curve gives rise to a rationally connected foliation of the manifold. In this note we show that, conversely, a movable curve can be found so that the maximal rationally connected fibration of the manifold may be recovered...

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