for this workshop
Transversality in contact homology
American Institute of Mathematics, Palo Alto, California
Joel Fish, Michael Hutchings, Joanna Nelson, and Katrin Wehrheim
This workshop, sponsored by AIM and the NSF, 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.
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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