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Representation Variety for the Rank One Affine Group
Ist Teil von
Mathematical Analysis in Interdisciplinary Research, 2022, Vol.179, p.381-416
Ort / Verlag
Switzerland: Springer International Publishing AG
Erscheinungsjahr
2022
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
The aim of this chapter is to study the virtual classes of representation varieties of surface groups onto the rank one affine group. We perform this calculation by three different approaches: the geometric method, based on stratifying the representation variety into simpler pieces; the arithmetic method, focused on counting their number of points over finite fields; and the quantum method, which performs the computation by means of a Topological Quantum Field Theory. We also discuss the corresponding moduli spaces of representations and character varieties, which turn out to be non-equivalent due to the non-reductiveness of the underlying group.