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Journal Article

Naturality of Heegaard Floer invariants under positive rational contact surgery


Tosun,  Bülent
Max Planck Institute for Mathematics, Max Planck Society;

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Mark, T. E., & Tosun, B. (2018). Naturality of Heegaard Floer invariants under positive rational contact surgery. Journal of Differential Geometry, 110(2), 281-344. doi:10.4310/jdg/1538791245.

Cite as: https://hdl.handle.net/21.11116/0000-0003-C51C-0
For a nullhomologous Legendrian knot in a closed contact 3-manifold Y we consider a contact structure obtained by positive rational contact surgery. We prove that in this situation the Heegaard Floer contact invariant of Y is mapped by a surgery cobordism to the contact invariant of the result of contact surgery, and we characterize the spin-c structure on the cobordism that induces the relevant map. As a consequence we determine necessary and
sufficient conditions for the nonvanishing of the contact invariant after rational surgery when Y is the standard 3-sphere, generalizing previous results of Lisca-Stipsicz and Golla. In fact, our methods allow direct calculation of the contact invariant in terms of the rational surgery mapping cone of Ozsváth and Szabó. The proof involves a construction called reducible open book surgery, which reduces in special cases to the capping-off construction studied by Baldwin.