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.