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

2021/09/03 by Tao Su, Su, Tao
Mathematics · #14F45 (Primary) 53D42 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2109.01645

openalex publication_date 2021/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Geometric P=W conjecture in the Painlev 'e cases via plumbing\n calculus

Related

• Cell decomposition and dual boundary complexes of character varieties
• On the geometric P=W conjecture
• The dual boundary complex of the SL₂ character variety of a punctured sphere
• The Geometric P=W conjecture and Thurston's compactification
• P=W phenomena on abelian varieties