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Contact Invariants in Floer Homology

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Contact and Symplectic Topology

Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 26))

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Abstract

In a pair of seminal papers Peter Ozsváth and Zoltan Szabó defined a collection of homology groups associated to a 3-manifold they named Heegaard-Floer homologies. Soon after, they associated to a contact structure ξ on a 3-manifold, an element of its Heegaard-Floer homology, the contact invariant c(ξ). This invariant has been used to prove a plethora of results in contact topology of 3-manifolds. In this series of lectures we introduce and review some basic facts about Heegaard Floer Homology and its generalization to manifolds with boundary due to Andras Juhász, the Sutured Floer Homology. We use the open book decompositions in the case of closed manifolds, and partial open book decompositions in the case of contact manifolds with convex boundary to define contact invariants in both settings, and show some applications to fillability questions.

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Acknowledgements

I want to thank the organizers for inviting me to give this lecture series, and to Laura Starkston for sharing her notes from the lectures. Thanks go to my collaborators Ko Honda and Will Kazez for all the interesting mathematics we did together that resulted in many results mentioned in these notes, and for originally drawing many figures that appear here, as well as to Whitney George and David Gay for help with some of the figures. Finally, thanks to Margaret Symington for reading the original draft and suggesting many improvements.

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Authors and Affiliations

  1. University of Georgia, Athens, GA, 30602, USA

    Gordana Matić

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  1. Gordana Matić
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Correspondence to Gordana Matić .

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Editors and Affiliations

  1. Laboratoire de Mathématiques d'Orsay, Université Paris-Sud, Orsay, France

    Frédéric Bourgeois

  2. Lab. de Mathématiques Jean Leray UMR6629, University of Nantes, Nantes, France

    Vincent Colin

  3. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

    András Stipsicz

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Matić, G. (2014). Contact Invariants in Floer Homology. In: Bourgeois, F., Colin, V., Stipsicz, A. (eds) Contact and Symplectic Topology. Bolyai Society Mathematical Studies, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-02036-5_6

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