Cyclic homology and symplectic topology
November 9 to November 13, 2009
American Institute of Mathematics,
Palo Alto, California
and Paul Seidel
This workshop will be devoted to a significant ongoing development on the interface between algebra and geometry through the realization that the ``closed string'' invariants of symplectic and contact manifolds, obtained by counting periodic orbits,can often be thought of algebraically as versions of Hochschild homology and cyclic homology. The relevant algebraic techniques originated outside symplectic topology (for instance, see the work of Goodwillie and Jones on free
loop space cohomology), but the connection has become increasingly close with the development of string topology and symplectic field
theory (see recent work of Godin and Cohen on one side, and of
Latschev and Cieliebak on the other).
This workshop will bring together specialists on the symplectic and
algebraic sides with the primary purposes of understanding this emerging picture. We expect to discuss implications for the structure of symplectic invariants, as well as concrete geometric applications. Two specific issues ofinterest will be
- conjectures of Seidel describing symplectic homology as
Hochschild homology, in the context of Lefschetz fibrations;
- recent work of Bourgeois-Ekholm-Eliashberg which constructs an exact
sequence for contact homology under critical handle attachments.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.