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.

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