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Symmetries and stabilization for sheaves of vanishing cycles
Journal of Singularities. 2015. Vol. 11. P. 85-151.
We study symmetries and stabilization properties of perverse sheaves of vanishing cycles of a regular function on a smooth C-scheme. We also generalize our results to replace the smooth scheme by a complex analytic space, and consider D-modules or mixed Hodge modules. We discuss applications to categorifying Donaldson--Thomas invariants of Calabi-Yau 3-folds, and to defining a 'Fukaya category' of Lagrangians in a complex symplectic manifold using perverse sheaves.