On the immersion classes of nearby Lagrangians

Abstract

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.

14 pages. Minor revisions in the second version. Minor revisions in the third version and accepted for publication by the Journal of Topology

References in corpus (2)

• Parametrized Ring-Spectra and the Nearby Lagrangian Conjecture
• Exact Lagrangian immersions with a single double point

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