On the immersion classes of nearby Lagrangians

Mohammed Abouzaid, Thomas Kragh

Published 2013-05-29, updated 2014-12-11Version 2

We show that the transfer map on Floer homotopy types associated to an exact Lagrangian embedding is an equivalence. This provides an obstruction to representing isotopy classes of Lagrangian immersions by Lagrangian embeddings, which, unlike previous obstructions, is sensitive to information that cannot be detected by Floer cochains. We show this by providing a concrete computation in the case of spheres.