Event Series
Event Type
Seminar
Monday, May 20, 2019 4:00 PM
Scott Zhang

Contact homology is an invariant of contact manifolds, constructed by counting punctured J-holomorphic curves in the symplectization. In 2015, Pardon developed a foundational framework called implicit atlas and virtual fundamental cycle (VFC), and applied it to rigorously define contact homology in the case when Reeb orbits are non-degenerate, addressing transversality issues.
 
In the Morse-Bott case, when Reeb orbits come in families of manifolds, contact homology was first defined by Bourgeois. In this talk, I will use Pardon's VFC technique to construct Morse-Bott contact homology. I will explain how to define an implicit atlas on the moduli spaces of "cascades", what is VFC, and how to extract virtual moduli counts in order to define the contact homology differential.