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Cell decomposition and dual boundary complexes of character varieties
The weak geometric P=W conjecture of Katzarkov--Noll--Pandit--Simpson asserts that for any smooth Betti moduli space $\mathcal{M}_B$ of complex dimension $d$ associated to a punctured Riemann surface, the dual boundary complex $\mathbb{D}\partial\mathcal{M}_B$ is homotopy equivalent to a $(d-1)$-sph
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