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# Joanna Nelson (Columbia/Barnard), Triangle Topology Seminar

## November 15, 2016 @ 5:15 pm - 6:15 pm

**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.