ScalingStacks

Theorem 3.28 . [04BI]

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Theorem 3.28.

(Floer theoretic obstruction, relaxing positivity condition) Assume the automatic transversality holds for the bordism current 𝒞\mathcal{C} between LL and L′L^{\prime}. Then the Lagrangian phase angle of LL has a lower bound on its oscillation:

supLθL≥max⁡{θ^1+,θ^1−},infLθL≤min⁡{θ^2+,θ^2−}.\sup_{L}\theta_{L}\geq\max\{\hat{\theta}_{1}^{+},\hat{\theta}_{1}^{-}\},\quad\inf_{L}\theta_{L}\leq\min\{\hat{\theta}_{2}^{+},\hat{\theta}_{2}^{-}\}.

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