Ana Rechtman
The Weinstein conjecture in the presence of submanifolds having a Legendrian foliation.
Tue, 04/05/2011 - 15:01 — SomNambulAuthors: Ana Rechtman, Klaus Niederkrüger
Subjects: Dynamical Systems
AbstractHelmut Hofer introduced in '93 a novel technique based on holomorphic curves
to prove the Weinstein conjecture. Among the cases where these methods apply
are all contact 3--manifolds $(M,\xi)$ with $\pi_2(M) \ne 0$. We modify Hofer's
argument to prove the Weinstein conjecture for some examples of higher
dimensional contact manifolds. In particular, we are able to show that the
connected sum with a real projective space always has a closed contractible
Reeb orbit.Minimal F{\o}lner foliations are amenable.
Tue, 01/19/2010 - 16:01 — SomNambulAuthors: Fernando Alcalde Cuesta, Ana Rechtman
Subjects: Dynamical Systems
AbstractFor finitely generated groups, amenability and F{\o}lner properties are
equivalent. However, contrary to a widespread idea, Kaimanovich showed that F\o
lner condition does not imply amenability for discrete measured equivalence
relations. He also gave an example of a $C^\infty$ foliation that is F{\o}lner
and non-amenable with respect to a non-finite transverse invariant measure. In
this paper, we exhibit two examples of $C^\infty$ foliations of closed
manifolds satisfying the same properties with respect to a finite transverse
invariant measure and a transverse invariant volume.
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