Title: Almost contact 5-manifolds are contact.
Author(s): Roger Casals (MIT), Dishant M. Pancholi (Chennai Mathematical Institute), Francisco Presas (CSIC-ICMAT).
Source: Annals of Mathematics. Pages 429-490 from Volume 182 (2015), Issue 2.
Date of publication: July 30, 2015.
Abstract: The existence of a contact structure is proved in any homotopy class of almost contact structures on a closed 5-dimensional manifold.
Roger Casals. Currently he is a CLE Moore Instructor at the MIT Department of Mathematics. He have completed his PhD thesis under the supervision of Francisco Presas at the ICMAT. In 2016 he has received the two main prizes for young researchers in Mathematics in Spain: the Jose Luís Rubio de Francia Prize and the Vicente Caselles prize (BBVA-RSME). His main research interests are: contact and symplectic topology, flexible-rigid dichotomy, h-principles and groups of contactomorphisms. He is also interested in the relations with algebraic geometry, including mirror symmetry and singularity theory.
Francisco Presas. Francisco Presas is a Permanent Researcher at the Instituto de CienciasMatemáticas – ICMAT (Institute for Mathematical Research). His current research interests lie in differential geometry, in particular symplectic and contact topology. He has published around 25 research articles, in Journals such as Journal of Differential Geometry, Geometry and Topology, Krelle, Annals of Mathematics, etc. He has published papers in algebraic geometry, symplectic geometry, contact topology, geometric quantization, etc. He is a well-known expert in the use of "approximately holomorphic techniques" in contact and symplectic topology. He has quite recently provided a number of results about flexibility in contact and Engel topology, contributing to create and develop that field. Francisco Presas obtained his Ph. D. thesis in Mathematics at Universidad Complutense de Madrid in 2000. He has held full-time academic positions at Stanford University (post-doc visitor), Universidad Autónoma de Madrid (Ramón y Cajal position) and ICMAT.