Gromov compactness for squiggly strip shrinking in pseudoholomorphic quilts

摘要

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(infinity)-bifunctor, in particular the associated Hoer complexes are isomorphic after a figure eight correction of the bounding cochain. An appendix with Felix Schmaschke provides examples of nontrivial figure eight bubbles.