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 SL2(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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