Journal of Symplectic Geometry

Volume 16 (2018)

Number 2

Exact, graded, immersed Lagrangians and Floer theory

Pages: 357 – 438

DOI: https://dx.doi.org/10.4310/JSG.2018.v16.n2.a2

Authors

Garrett Alston (Department of Mathematics, University of Oklahoma, Norman, Ok., U.S.A.)

Erkao Bao (Department of Mathematics, University of California at Los Angeles)

Abstract

We develop Lagrangian Floer Theory for exact, graded, immersed Lagrangians with clean self-intersection using Seidel’s setup. A positivity assumption on the index of the self intersection points is imposed to rule out certain (but not all) disc bubbles. This allows the Lagrangians to be included in the exact Fukaya category. We also study quasi-isomorphism of Lagrangians under certain exact deformations which are not Hamiltonian.

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Both authors were supported by the Institute of Mathematical Sciences, Chinese University of Hong Kong while this work was partially completed.

Received 31 August 2014

Accepted 10 November 2017

Published 18 July 2018