ScalingStacks

Definition 3.32 . [04BU]

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Definition 3.32.

Let LL be an almost calibrated exact Lagrangian brane representing a class in the (suitably enlarged) derived Fukaya category. Suppose for any almost calibrated exact Lagrangian objects L1,L2L_{1},L_{2} fitting into a distinguished triangle L1→L→L2→L1​[1]L_{1}\to L\to L_{2}\to L_{1}[1], we always have

θ^1=arg∫L1Ω≤θ^2=∫L2Ω,resp. θ^1=arg∫L1Ω<θ^2=∫L2Ω,\hat{\theta}_{1}=\arg\int_{L_{1}}\Omega\leq\hat{\theta}_{2}=\int_{L_{2}}\Omega,\quad\text{resp. }\hat{\theta}_{1}=\arg\int_{L_{1}}\Omega<\hat{\theta}_{2}=\int_{L_{2}}\Omega,

then we say LL is Thomas-Yau semistable (resp. strictly stable). If LL fails to be Thomas-Yau semistable, we say it is Thomas-Yau unstable.

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