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