A new SymPy-based package for simplifying lambda-ring expressions is used to verify Mozgovoy's motivic formula for twisted Higgs bundles up to genus 18 and rank 3.
Motivic theory of representation varieties via Topological Quantum Field Theories
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abstract
In this paper, we use lax monoidal TQFTs as an effective computational method for motivic classes of representation varieties. In particular, we perform the calculation for parabolic $\mathrm{SL}_2(\mathbb{C})$-representation varieties over a closed orientable surface of arbitrary genus and any number of marked points with holonomies of Jordan type. This technique is based on a building method of lax monoidal TQFTs of physical inspiration that generalizes the construction of Gonz\'alez-Prieto, Logares and Mu\~noz.
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Motives meet SymPy: studying $\lambda$-ring expressions in Python
A new SymPy-based package for simplifying lambda-ring expressions is used to verify Mozgovoy's motivic formula for twisted Higgs bundles up to genus 18 and rank 3.