Dual boundary complexes of Betti moduli spaces over the two-sphere with one irregular singularity

Abstract

The weak geometric P=W conjecture of L. Katzarkov, A. Noll, P. Pandit, and C. Simpson states that, a smooth Betti moduli space of complex dimension $d$ over a punctured Riemann surface has the dual boundary complex homotopy equivalent to a sphere of dimension $d-1$. Via a microlocal geometric perspective, we verify this conjecture for a class of rank $n$ wild character varieties over the two-sphere with one puncture, associated with any Stokes Legendrian link defined by an $n$-strand positive braid.

Revised version: 34 pages, 10 figures; The revised version has undergone significant changes: A more general result, devoid of connected braid closures, has been proven. The proof is now simpler and more natural, utilizing braid varieties in place of augmentation varieties

References in corpus (10)

• Symplectic Manifolds and Isomonodromic Deformations
• Quasi-Hamiltonian Geometry of Meromorphic Connections
• Legendrian knots and constructible sheaves
• Cluster varieties from Legendrian knots
• Existence of moduli spaces for algebraic stacks
• Arithmetic harmonic analysis on character and quiver varieties
• The dual complex of Calabi--Yau pairs
• Augmentations are Sheaves
• Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
• Ruling polynomials and augmentations over finite fields