Motivic theory of representation varieties via Topological Quantum Field Theories

\'Angel Gonz\'alez-Prieto

Motivic theory of representation varieties via Topological Quantum Field Theories

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arxiv 1810.09714 v2 pith:RJN6DDG4 submitted 2018-10-23 math.AG math-phmath.CTmath.MPmath.RT

Ángel González-Prieto This is my paper · ORCID

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keywords representationvarietiesmethodmonoidalmotivictqftsalez-prietoarbitrary

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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
math.AG 2024-12 conditional novelty 5.0 of 10

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.

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