Joanna Nelson (Columbia/Barnard), Triangle Topology Seminar

Title:  An integral lift of cylindrical contact homology

Abstract: I will discuss joint work with Hutchings which gives a rigorous construction of cylindrical contact homology via geometric methods. This talk will highlight our use of non-equivariant constructions, automatic transversality, and obstruction bundle gluing. Together these yield a nonequivariant homological contact invariant which is expected to be isomorphic to $SH^+$ under suitable assumptions. By making use of family Floer theory we obtain an $S^1$-equivariant theory defined over $\mathbb{Z}$ coefficients, which when tensored with $\mathbb{Q}$ recovers the classical cylindrical contact homology, now with the guarantee of well-definedness and invariance. This integral lift of contact homology also contains interesting torsion information.