Contact topology in higher dimensions
May 21 to May 25, 2012
American Institute of Mathematics,
San Jose, California
and Klaus Niederkrueger
This workshop will be devoted to developing
high dimensional contact topology. While the existence of contact structures
on 3-manifolds is well understood and we know quite a lot about properties of
contact structures on 3-manifolds, very little is known about the nature of
high dimensional contact topology, and even the basic existence questions for
contact structures on higher dimensional manifolds are unknown except in a few
The main topics for the workshop are
While little is known about any of this topics, there has recently been
promising progress on all of them. This workshop will bring together experts
in contact topology (especially ones contributing to the progress on these
higher dimensional questions) as well as experts in high dimensional topology,
symplectic field theory, and related areas, to energize research in high
dimensional contact geometry.
- The existence of contact structures on all odd dimensional manifolds.
- The exploration of the number and type of contact structures a given
manifold can support.
- The study of Legendrian submanifolds of a contact manifold.
- The non-squeezing phenomenon.
- The investigation of symplectic fillings in high dimensions.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
Slides from the talk The Existence Problem by Giroux.
Problem list prepared by Sylvain Courte.
Papers arising from the workshop:
The discriminant and oscillation lengths for contact and Legendrian isotopies
by Vincent Colin and Sheila Sandon, J. Eur. Math. Soc. (JEMS) 17 (2015), no. 7, 1657-1685 MR3361726
Quantitative Darboux theorems in contact geometry
by John B. Etnyre, Rafal Komendarczyk, and Patrick Massot
Loose Legendrians and the plastikstufe
by Emmy Murphy, Klaus Niederkr�ger, Olga Plamenevskaya, and Andr�s I. Stipsicz, Geom. Topol. 17 (2013), no. 3, 1791-1814 MR3073936