Description
Fool’s crowns, Schwarzian, and topological recursion.
For a Riemann surface with holes, we propose a variant of the action on a circumference-P boundary component with n bordered cusps attached (a “fool’s crown”) that is decoration-independent and generates finite volumes V crown of the corresponding moduli spaces when integrated against the volume n,P form obtained by inverting the Fenchel--Nielsen (Goldman) Poisson bracket on a set of decoration-independent combinations of Penner’s \lambda lengths. In the limit as n \to ∞, the integrals transform into a functional integral with the measure containing the Schwarzian and reproducing the measure by Stanford—Witten and Alekseev--Meinrenken. I will discuss hypothetical links to topological recursion systems and the volumes of moduli spaces for a disc with n bordered cusps. Based on arXiv.2411.03913.
