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Covariantly functorial wrapped Floer theory on Liouville sectors

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Abstract

We introduce a class of Liouville manifolds with boundary which we call Liouville sectors. We define the wrapped Fukaya category, symplectic cohomology, and the open-closed map for Liouville sectors, and we show that these invariants are covariantly functorial with respect to inclusions of Liouville sectors. From this foundational setup, a local-to-global principle for Abouzaid’s generation criterion follows.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Southern California, Los Angeles, CA, 90089, USA

    Sheel Ganatra

  2. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    John Pardon

  3. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    Vivek Shende

Authors
  1. Sheel Ganatra
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  2. John Pardon
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  3. Vivek Shende
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Additional information

S. G. was partially supported by the National Science Foundation through a postdoctoral fellowship with grant number DMS-1204393 and under agreement number DMS-1128155. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

This research was conducted during the period J. P. served as a Clay Research Fellow and was partially supported by a Packard Fellowship and by the National Science Foundation under the Alan T. Waterman Award, Grant No. 1747553.

V. S. is partially supported by the NSF grant DMS-1406871 and a Sloan fellowship.

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Ganatra, S., Pardon, J. & Shende, V. Covariantly functorial wrapped Floer theory on Liouville sectors. Publ.math.IHES 131, 73–200 (2020). https://doi.org/10.1007/s10240-019-00112-x

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