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. We also extend the result to the parabolic case with any number of punctures and arbitrary monodromies. As a 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 that can be applied to other situations.

中文翻译：

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表示变体的单调单调拓扑量子场理论

我们构建了一个松散的单调拓扑量子场论，该理论计算任何闭合流形的基本群到任何复杂代数群G的表示形式的Deligne-Hodge多项式。我们还将结果扩展到具有任意数量的穿孔和任意一元曲线的抛物线情况。作为副产品，我们根据G上混合Hodge模空间之间的同态来获得这些多项式的公式。该构造是在可以应用于其他情况的分类理论框架中开发的。