arXiv subjects

Roger Casals

Publications and source records attributed to Roger Casals.

44 records · Page 3Linked to original sources

arXiv2015

Chern-Weil theory and the group of strict contactomorphisms

In this paper we study the groups of contactomorphisms of a closed contact manifold from a topological viewpoint. First we construct examples of contact forms on spheres whose Reeb flow has a dense orbit. Then we show that the unitary group U(n+1) is homotopically essential in the group of contactomorphisms of the standard contact sphere S^(2n+1) and prove that in the case of the 3-sphere the contactomorphism group is in fact homotopy equivalent to U(2). In the second part of the paper we focus on the group of strict contactomorphisms -- using the framework of Chern-Weil theory we introduce and study contact characteristic classes analogous to the Reznikov Hamiltonian classes in symplectic topology. We carry out several explicit calculations illustrating non-triviality of the contact classes.

math.SG↗

arXiv2014

Almost contact 5-folds are contact

We prove that every homotopy class of almost contact structures on a closed 5-dimensional manifold admits a contact structure.

math.SG↗

arXiv2014

On the strong orderability of overtwisted 3-folds

In this article we address the existence of positive loops of contactomorphisms in overtwisted contact 3-folds. We present a construction of such positive loops in the contact fibered connected sum of certain contact 3-folds along transverse knots. In particular, we obtain positive loops of contactomorphisms in overtwisted contact structures.

math.SG↗

arXiv2014

H-principle for 4-dimensional contact foliations

In this article we introduce the topological study of codimension-1 foliations which admit contact or symplectic structures on the leaves. A parametric existence h-principle for foliated contact structures is provided for any cooriented foliation in a closed oriented 4-fold.

math.SG↗

arXiv2014

On the non-existence of small positive loops of contactomorphisms on overtwisted contact manifolds

We prove that on overtwisted contact manifolds there can be no positive loops of contactomorphisms that are generated by a $C^0$-small Hamiltonian function.

math.SG↗

arXiv2014

Overtwisted Disks and Exotic Symplectic Structures

The symplectization of an overtwisted contact structure in Euclidean 3--space is shown to be an exotic symplectic structure on Euclidean 4--space. The technique can be extended to produce exotic symplectic structures in higher dimensional Euclidean spaces using a GPS--structure and applies to symplectizations of appropriate open contact manifolds.

math.SG↗

arXiv2013

A Remark on the Reeb Flow for Spheres

We prove the non--triviality of the Reeb flow for the (2n+1)--dimensional standard contact spheres inside the fundamental group of their contactomorphism group, n greater than 3. The argument uses the existence of homotopically non--trivial 2--spheres in the space of contact structures of a 3--Sasakian manifold.

math.SG↗

arXiv2013

Contact Blow-Up

We provide various definitions for the contact blow--up. Such different approaches to the contact blow--up are related. Some uniqueness and non--uniqueness results are also provided.

math.SG↗