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  MR3543703
Algebraic 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