Acta Mathematica

Volume 220 (2018)

Number 2

Simple homotopy equivalence of nearby Lagrangians

Pages: 207 – 237



Mohammed Abouzaid (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Thomas Kragh (Department of Mathematics, Uppsala University, Uppsala, Sweden)


Given a closed exact Lagrangian in the cotangent bundle of a closed smooth manifold, we prove that the projection to the base is a simple homotopy equivalence.


exact Lagrangian embedding, cotangent bundle, spectral sequence

M. A. was supported by NSF grant DMS-1308179, and by Simons Foundation grant 385571. The authors were hosted by the Mittag-Leffler Institute during its “Symplectic Geometry and Topology” program in Fall 2015.

Received 17 March 2016

Received revised 23 October 2017

Accepted 6 December 2017

Published 16 August 2018