Holomorphic curves and continuation maps in Liouville bundles

Abstract

We construct an unwrapped Floer theory for bundles of Liouville sectors. In particular, we construct a compatible collection of unwrapped Fukaya categories of fibers of a Liouville bundle, and prove that the two natural constructions of continuation maps in this setting behave compatibly. These constructions are exploited in [OT19] to construct homotopically coherent actions of Lie groups on wrapped Fukaya categories, thereby proving a conjecture from Teleman's 2014 ICM address.

44 pages, 4 figures. Comments welcome! Portions of this work previously appeared in arXiv:1911.00349v2; the previous work has been split into multiple papers to better exposit the ingredients