Motivic theory of representation varieties via Topological Quantum Field Theories

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 González-Prieto, Logares and Muñoz.

arXiv comment40 pages, 5 figures. v2 change of title and major improvements. Extended to computation of motivic classes, removed Section 2 and added Section 3

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Cited by in corpus (5)

• Virtual classes of parabolic ${\mathrm{SL}}_2(\mathbb{C})$-character varieties
• Representation variety for the rank one affine group
• Virtual Classes of Representation Varieties of Upper Triangular Matrices via Topological Quantum Field Theories
• Pseudo-quotients of algebraic actions and their application to character varieties
• The point counting problem in representation varieties of torus knots