Lagrangian Floer homology on symplectic blow ups

We show how to compute the Lagrangian Floer homology in the one-point blow up of the proper transform of Lagrangians submanifolds, solely in terms of information of the base manifold. As an example we present an alternative computation of the Lagrangian quantum homology in the one-point blow up of $(\mathbb{C}P^2, \omega_{FS})$ of the proper transform of the Clifford torus.

Keywords

Lagrangian Floer homology, symplectic blow up, holomorphic discs

2010 Mathematics Subject Classification

53D12, 53D40, 57R58

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The author was partially supported by CONACYT grants ERC-291755 and CB-A1-S-8803.

Received 15 March 2019

Accepted 22 May 2019

Published 8 September 2020