ScalingStacks

Definition 5.1 [058A]

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Definition 5.1

Take graded Lagrangians (L1,θ1)(L_{1},\theta_{1}) and (L2,θ2)(L_{2},\theta_{2}), hamiltonian isotoped to intersect cleanly, and such that the graded (relative) Lagrangian connect sums (L1​#​L2,θ1​#​θ2)(L_{1}\#L_{2},\theta_{1}\#\theta_{2}) exist as above. Then a Lagrangian LL of Maslov class zero is said to be destabilised by the LiL_{i} if it is hamiltonian isotopic to such an L1​#​L2L_{1}\#L_{2}, and the phases (real numbers, induced by the gradings) satisfy

ϕ⁡(L1)≥ϕ⁡(L2).\phi(L_{1})\geq\phi(L_{2}).

If LL is not destabilised by any such LiL_{i} then it is called stable.

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