On character varieties of singular manifolds

In this paper, we construct a lax monoidal Topological Quantum Field Theory that computes virtual classes, in the Grothendieck ring of algebraic varieties, of G -representation varieties over manifolds with conic singularities, which we call nodefolds. This construction is valid for any algebraic gr...

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Bibliographic Details
Published in:Research in the mathematical sciences 2023-09, Vol.10 (3), Article 32
Main Authors: González-Prieto, Ángel, Logares, Marina
Format: Article
Language:English
Subjects:
Algebra
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Manifolds (mathematics)
Mathematics
Mathematics and Statistics
Quantum theory
Representations
Singularity (mathematics)
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Summary:In this paper, we construct a lax monoidal Topological Quantum Field Theory that computes virtual classes, in the Grothendieck ring of algebraic varieties, of G -representation varieties over manifolds with conic singularities, which we call nodefolds. This construction is valid for any algebraic group G , in any dimension and also in the parabolic setting. In particular, this TQFT allows us to compute the virtual classes of representation varieties over complex singular planar curves. In addition, in the case G = SL 2 ( k ) , the virtual class of the associated character variety over a nodal closed orientable surface is computed both in the non-parabolic and parabolic scenarios.
ISSN:2522-0144
2197-9847
DOI:10.1007/s40687-023-00394-y