Transversality in contact homology
December 8 to December 12, 2014
at the
American Institute of Mathematics,
San Jose, California
organized by
Joel Fish,
Michael Hutchings,
Joanna Nelson,
and Katrin Wehrheim
Original Announcement
This workshop will bring together specialists in symplectic and contact topology with the
goals of clarifying the gaps in current arguments concerning the definition of
contact homology and of moving forward to fill these gaps and build precise
foundations for the cylindrical, linearized, local and possibly other versions
of contact homology. The lack of established transversality results for multiply
covered curves and their branched covers obstruct the existence of chain
complexes except in specialized circumstances in dimension 3 as well as
invariance of all homology theories for contact manifolds that are based on
pseudoholomorphic curves.
The main focus of this workshop will be to evaluate and rigidify the reach of
traditional methods, which make use of concrete geometric perturbations such as
automatic transversality, obstruction bundle gluing, domain dependent almost
complex structures, and Donaldson divisors. Given that we plan to isolate the
parts of contact homology which do not require further refined regularization
methods than the aforementioned geometric methods, we will not discuss the use
of Kuranishi structures or polyfolds during the workshop.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
Papers arising from the workshop:
My Contact Homology Shopping List
by Viktor L. Ginzburg
Brieskorn Manifolds, Positive Sasakian Geometry, and Contact Topology
by Charles P. Boyer, Leonardo Macarini and Otto van Koert,
Forum Math. 28 (2016), no. 5, 943-965 MR3543703Algebraic torsion via Heegaard Floer homology
by Cagatay Kutluhan, Gordana Matic, Jeremy Van Horn-Morris and Andy Wand, Breadth in Contemporary Topology (proceedings of the 2017 Georgia International Topology Conference, Proceedings of Symposia in Pure Mathematics, AMS
