Cylindrical contact homology as a well-defined homology?

Princeton/IAS Symplectic Geometry Seminar
Topic:Cylindrical contact homology as a well-defined homology?
Speaker:Joanna Nelson
Affiliation:Member, School of Mathematics
Date:Friday, February 7
Time/Room:1:30pm - 2:30pm/S-101
Video Link:https://video.ias.edu/pisgs/2014/0207-JoannaNelson

In this talk I will explain how the heuristic arguments sketched in literature since 1999 fail to define a homology theory. These issues will be made clear with concrete examples and we will explore what stronger conditions are necessary to develop a theory without the use of virtual chains or polyfolds in 3 dimensions. It turns out that this can be accomplished by placing strong conditions on the growth rates of the indices of Reeb orbits. In addition we sketch a new approach allowing us to compute cylindrical contact for a large class of examples which admit contact forms that are admissible under the stronger conditions required. This approach is applicable to prequantization spaces and the links of simple singularities.