The weights of the tautological classes of character varieties

TL;DR

This paper computes the weights of tautological classes in character varieties by applying the functorial mixed Hodge structure on simplicial schemes, advancing understanding of their geometric and topological properties.

Contribution

It introduces a method to determine the weights of tautological classes in character varieties using functorial mixed Hodge structures on simplicial schemes, providing new computational tools.

Findings

Weights of tautological classes explicitly calculated

Method applied to specific character varieties

Enhances understanding of mixed Hodge structures in algebraic geometry

Abstract

I calculate the weights of the tautological classes of character varieties using the functorial mixed Hodge structure on simplicial schemes.