Picard-Lefschetz theory and dilating C^*-actions

Abstract

We consider C^*-actions on Fukaya categories of exact symplectic manifolds. Such actions can be constructed by dimensional induction, going from the fibre of a Lefschetz fibration to its total space. We explore applications to the topology of Lagrangian submanifolds, with an emphasis on ease of computation.

v3: appendectomy performed; to appear in Journal of Topology

References in corpus (4)

• The symplectic arc algebra is formal
• Disjoinable Lagrangian spheres and dilations
• Infinity inner products on A-infinity algebras
• Floer cohomology of $\mathfrak{g}$-equivariant Lagrangian branes

Cited by in corpus (8)

• Koszul duality patterns in Floer theory
• Legendrian Fronts for Affine Varieties
• q-Stability conditions on Calabi-Yau-X categories
• $q$-Stability conditions via $q$-quadratic differentials for Calabi-Yau-$\mathbb{X}$ categories
• A simplicial construction of G-equivariant Floer homology
• Koszul duality via suspending Lefschetz fibrations
• Exact Calabi-Yau categories and odd-dimensional Lagrangian spheres
• Disjoinable Lagrangian tori and semisimple symplectic cohomology