Summer School 2015: Moduli Problems in Symplectic Geometry

Collection Summer School 2015: Moduli Problems in Symplectic Geometry

Organizer(s) J. Nelson (Columbia University and the Institute for Advanced Study), D. Cristofaro-Gardiner (Harvard University), J. Fish (Institute for Advanced Study and UMass Boston)

Date(s) 06/07/2015 - 17/07/2015

linked URL https://indico.math.cnrs.fr/event/585/

00:00:00 / 00:00:00

8 36

An Integral lift of contact homology

By Joanna Nelson

Cylindrical contact homology is arguably one of the more notorious Floer-theoretic constructions. The past decade has been less than kind to this theory, as the growing knowledge of gaps in its foundations has tarnished its claim to being a well-defined contact invariant. However, jointly with Hutchings we have managed to redeem this theory in dimension 3 for dynamically convex contact manifolds. This talk will highlight our implementation of non-equivariant constructions, domain dependent almost complex structures, automatic transversality, and obstruction bundle gluing, yielding a homological contact invariant which is expected to be isomorphic to $SH^+$ under suitable assumptions, though it does not require a filling of the contact manifold. By making use of family Floer theory we obtain an $S^1$-equivariant theory defined over Z coefficients, which when tensored with Q yields cylindrical contact homology, now with the guarantee of well-definedness and invariance.

Information about the video

Date of recording 10/07/2015
Date of publication 16/07/2015
Institution IHES
Format MP4

Domain(s)

Symplectic Geometry

MSC codes

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