Gromov compactness for squiggly strip shrinking in pseudoholomorphic quilts

• Nathaniel Bottman ^[1] ; Katrin Wehrheim ^[2]
  1. [1] Institute for Advanced Study

     Institute for Advanced Study

     Estados Unidos

     
  2. [2] University of California, USA
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 4, 2018, págs. 3381-3443
• Idioma: inglés
• DOI: 10.1007/s00029-018-0404-4
• Enlaces
  • Texto completo (pdf)
• Resumen

  • 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∞-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.