The Geometric P=W conjecture in the Painlevé cases via plumbing calculus

Abstract

We use plumbing calculus to prove the homotopy commutativity assertion of the Geometric P=W conjecture in all Painlevé cases. We discuss the resulting Mixed Hodge structures on Dolbeault and Betti moduli spaces.

12 pages, 6 figures, 1 table

References in corpus (2)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Simpson's geometric P=W conjecture in the Painlevé VI case via abelianization