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Special Seminar

Constructing Morse-Bott Contact Homology using virtual fundamental cycles

Scott Zhang (Stanford University)

Location:  Hill 705
Date & time: Tuesday, 16 April 2019 at 12:00PM - 1:00PM

Abstract:  Contact homology is an invariant of contact manifolds, constructed by counting punctured J-holomorphic curves in the symplectization of contact manifolds. Recently, Pardon have 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. Some key ingredients are a combinatorial description of stratification of moduli spaces of "cascades", and a gluing theorem of J-holomorphic curves.