arXiv subjects

Melanie Bertelson

Publications and source records attributed to Melanie Bertelson.

3 recordsLinked to original sources

arXiv2021

Conformal Symplectic structures, Foliations and Contact Structures

This paper presents two existence h-principles, the first for conformal symplectic structures on closed manifolds, and the second for leafwise conformal symplectic structures on foliated manifolds with non empty boundary. The latter h-principle allows to linearly deform certain codimension-$1$ foliations to contact structures. These results are essentially applications of the Borman-Eliashberg-Murphy h-principle for overtwisted contact structures and of the Eliashberg-Murphy symplectization of cobordisms, together with tools pertaining to foliated Morse theory, which are elaborated here.

math.SG↗

arXiv2000

A h-principle for open relations invariant under foliated isotopies

This paper presents a natural extension to foliated spaces of the following result due to Gromov : the h-principle for open, invariant differential relations is valid on open manifolds. The definition of openness for foliated spaces adopted here involves a certain type of Morse functions. Consequences concerning the problem of existence of regular Poisson structures, the original motivation for this work, are presented.

math.DG↗

arXiv2000

Foliations associated to regular Poisson structures

A regular Poisson manifold can be described as a foliated space carrying a tangentially symplectic form. Examples of foliations are produced here that are not induced by any Poisson structure although all the basic obstructions vanish.

math.DG↗