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 over a punctured Riemann surface has the dual boundary complex homotopy equivalent to a sphere of dimension . Via a microlocal geometric perspective, we verify this conjecture for a class of rank wild character varieties over the two-sphere with one puncture, associated with any Stokes Legendrian link defined by an -strand positive braid.
Cite
@article{arxiv.2109.01645,
title = {Dual boundary complexes of Betti moduli spaces over the two-sphere with one irregular singularity},
author = {Tao Su},
journal= {arXiv preprint arXiv:2109.01645},
year = {2025}
}
Comments
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