Cylindrical contact homology as a well-defined homology?

Friday, February 7, 2014 -
1:30pm to 2:30pm
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 homology 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.
Speaker: 
Jo Nelson
IAS
Event Location: 
IAS - Simonyi Hall Seminar Room SH-101