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Gromov compactness for squiggly strip shrinking in pseudoholomorphic quilts

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Abstract

We establish a Gromov compactness theorem for strip shrinking in pseudoholomorphic quilts when composition of Lagrangian correspondences is immersed. In particular, we show that figure eight bubbling occurs in the limit, argue that this is a codimension-0 effect, and predict its algebraic consequences—geometric composition extends to a curved \(A_\infty \)-bifunctor, in particular the associated Floer complexes are isomorphic after a figure eight correction of the bounding cochain. An appendix with Felix Schmäschke provides examples of nontrivial figure eight bubbles.

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Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, 1 Einstein Dr, Princeton, NJ, 08540, USA

    Nathaniel Bottman

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

    Katrin Wehrheim

Authors
  1. Nathaniel Bottman
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  2. Katrin Wehrheim
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Correspondence to Nathaniel Bottman.

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Bottman, N., Wehrheim, K. Gromov compactness for squiggly strip shrinking in pseudoholomorphic quilts. Sel. Math. New Ser. 24, 3381–3443 (2018). https://doi.org/10.1007/s00029-018-0404-4

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