ScalingStacks

Remark 2.14 . [0490]

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Remark 2.14.

The Joyce program suggests that running the LMCF would result in a sequence of exact isotopies and surgeries, to connect the initial Lagrangian to its infinite time limit, which one hopes to be the unique representative of the Harder-Narasimhan decomposition. In the almost calibrated case, there is no ‘collapsing zero object’ in this process for homological reasons, so the surgeries should be continuous in the geometric measure theory sense. Since any two such Lagrangians within the same Db​F​u​k​(X)D^{b}Fuk(X) class are expected to flow to the same limit, they are supposedly connected to each other through a continuous family of unobstructed Lagrangians.

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