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A refinement of the A-polynomial of quivers

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arxiv 1102.5308 v1 pith:GFZJ6L2V submitted 2011-02-25 math.RT

Fernando Rodriguez Villegas This is my paper · ORCID
classification math.RT
keywords a-polynomialformularefinementbettibundlescasecharacterconjecturally
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We study a refinement of the A-polynomial in the case of the g-loop quiver. We give an explicit formula for its value at q=1. Conjecturally this implies a formula for the middle Betti number of the moduli space of Higgs bundles or equivalently of the character variety of a Riemann surface of genus g.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Habiro ring of a number field

    math.NT 2024-12 conditional novelty 8.0 of 10

    A Habiro ring of a number field is constructed, with K3-graded modules, and perturbative quantum invariants are shown to be elements of these modules.

  2. Explicit classes in Habiro cohomology

    math.AG 2025-05 conditional novelty 7.0 of 10

    Explicit 'naive' Habiro cohomology classes are built from q-hypergeometric deformations and push-forwards, producing canonical q-deformations of Picard-Fuchs equations for Legendre, figure-eight A-polynomial, and quin...

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