A lax monoidal Topological Quantum Field Theory for representation varieties

Abstract

We construct a lax monoidal Topological Quantum Field Theory that computes Deligne-Hodge polynomials of representation varieties of the fundamental group of any closed manifold into any complex algebraic group $G$. As byproduct, we obtain formulas for these polynomials in terms of homomorphisms between the space of mixed Hodge modules on $G$. The construction is developed in a categorical-theoretic framework allowing its application to other situations.

26 pages, 4 figures. Added references. Added Section 5 with examples

References in corpus (1)

• Virtual classes of parabolic ${\mathrm{SL}}_2(\mathbb{C})$-character varieties

Cited by in corpus (8)

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• Virtual Classes of Character Stacks