48 citations · 205 across the 35 of their papers we have counts for
33 papers · 1 filter
An -principle for embeddings transverse to a contact structure
Robert Cardona, Francisco Presas
Given a class of embeddings into a contact or a symplectic manifold, we give a sufficient condition, that we call isocontact or isosymplectic realization, for this class to satisfy…
Spaces of tight contact structures in dimension 3
Eduardo Fernández, Javier Martínez-Aguinaga, Francisco Presas
We study spaces of tight contact structures and contactomorphism groups in dimension . We introduce a microfibration method for studying spaces of convex surfaces in contact …
The Legendrian Whitney trick
Roger Casals, Dishant M. Pancholi, Francisco Presas
In this article, we prove a Legendrian Whitney trick which allows for the removal of intersections between codimension-two contact submanifolds and Legendrian submanifolds, assumin…
Loops of Legendrians in contact 3-manifolds
Eduardo Fernández, Javier Martínez-Aguinaga, Francisco Presas
We study homotopically non-trivial spheres of Legendrians in the standard contact R3 and S3. We prove that there is a homotopy injection of the contactomorphism group of S3 into so…
Symplectic foliated fillings of sphere cotangent bundles
Francisco Presas, Sushmita Venugopalan
We classify symplectically foliated fillings of certain foliated manifolds with a contact structure on the leaves. We show that for the foliated sphere cotangent bundle of the Reeb…
Notes On Open Book Decompositions For Engel Structures
Vincent Colin, Francisco Presas, Thomas Vogel
We relate open book decompositions of a 4-manifold M with its Engel structures. Our main result is, given an open book decomposition of M whose binding is a collection of 2-tori an…
Tight neighborhoods of contact submanifolds
Luis Hernández-Corbato, Lucía Martín-Merchán, Francisco Presas
We prove that any small enough neighborhood of a closed contact submanifold is always tight under a mild assumption on its normal bundle. The non-existence of --small positive…
Loose Engel structures
Roger Casals, Álvaro del Pino, Francisco Presas
This article introduces the notion of a loose family of Engel structures and shows that two such families are Engel homotopic if and only if they are formally homotopic. This impli…
Fundamental groups of formal Legendrian and horizontal embedding spaces
Eduardo Fernández, Javier Martínez-Aguinaga, Francisco Presas
We compute the fundamental group of each connected component of the space of formal Legendrian embeddings in R3. We use it to show that previous examples in the literature of non t…
Geometric quantization of semitoric systems and almost toric manifolds
Eva Miranda, Francisco Presas, Romero Solha
Kostant gave a model for the real geometric quantization associated to polarizations via the cohomology associated to the sheaf of flat sections of a pre-quantum line bundle. This…
A simple construction of positive loops of Legendrians
Dishant Pancholi, José Luis Pérez, Francisco Presas
We construct positive loops of Legendrian submanifolds in several instances. In particular, we partially recover G. Liu's result stating that any loose Legendrian admits a positive…
Flexibility for tangent and transverse immersions in Engel manifolds
Alvaro del Pino, Francisco Presas
In this article we study immersions of the circle that are tangent to an Engel structure . We show that a full -principle does exist as soon as one excludes the clo…
The conjugation method in symplectic dynamics
Luis Hernández-Corbato, Francisco Presas
We prove the existence of minimal symplectomorphisms and strictly ergodic contactomorphisms on manifolds which admit a locally free --action by symplectomorphisms and…
Higher Maslov Indices
Roger Casals, Viktor L. Ginzburg, Francisco Presas
We define Maslov--type indices associated to contact and symplectic transformation groups. There are two such families of indices. The first class of indices are maps from the homo…
The foliated Weinstein conjecture
Álvaro del Pino, Francisco Presas
A foliation is said to admit a foliated contact structure if there is a codimension 1 distribution in the tangent space of the foliation such that the restriction to any leaf is co…
Existence h-principle for Engel structures
Roger Casals, Jose Luis Pérez, Álvaro del Pino +1
In this article we prove that the inclusion of the space of Engel structures of a smooth -fold into the space of full flags of its tangent bundle induces surjections in all homo…
Geometric criteria for overtwistedness
Roger Casals, Emmy Murphy, Francisco Presas
We establish geometric criteria to decide whether a contact manifold is overtwisted. Starting with the original definition, we first relate the different overtwisted disks in each…
On the strong orderability of overtwisted 3-folds
Roger Casals, Francisco Presas
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 fibe…
H-principle for 4-dimensional contact foliations
Roger Casals, Alvaro del Pino, Francisco Presas
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 fo…
On the non-existence of small positive loops of contactomorphisms on overtwisted contact manifolds
Roger Casals, Francisco Presas, Sheila Sandon
We prove that on overtwisted contact manifolds there can be no positive loops of contactomorphisms that are generated by a -small Hamiltonian function.
A Remark on the Reeb Flow for Spheres
Roger Casals, Francisco Presas
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. T…
Geometric Quantization of real polarizations via sheaves
Eva Miranda, Francisco Presas
In this article we develop tools to compute the Geometric Quantization of a symplectic manifold with respect to a regular Lagrangian foliation via sheaf cohomology and obtain impor…
Geometric decompositions of almost contact manifolds
Francisco Presas
These notes are intended to be an introduction to the use of approximately holomorphic techniques in almost contact and contact geometry. We develop the setup of the approximately…
Contact Blow-Up
Roger Casals, Dishant M. Pancholi, Francisco Presas
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 provide…