Dual boundary complexes of Betti moduli spaces over the two-sphere with one irregular singularity.(English)Zbl 07972364
Summary: 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.
MSC:
| 14F45 | Topological properties in algebraic geometry |
| 53Dxx | Symplectic geometry, contact geometry |
| 14Dxx | Families, fibrations in algebraic geometry |
| 34Mxx | Ordinary differential equations in the complex domain |
Keywords:
wild character variety;cell decomposition;dual boundary complex;weak geometric \(P = W\) conjecture;micro-support;Stokes Legendrian linkCite
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