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Representation Variety for the Rank One Affine Group

In: Mathematical Analysis in Interdisciplinary Research

Author

Listed:
  • Ángel González-Prieto

    (Universidad Complutense de Madrid)

  • Marina Logares

    (Universidad Complutense de Madrid)

  • Vicente Muñoz

    (Universidad de Málaga)

Abstract

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.

Suggested Citation

  • Ángel González-Prieto & Marina Logares & Vicente Muñoz, 2021. "Representation Variety for the Rank One Affine Group," Springer Optimization and Its Applications, in: Ioannis N. Parasidis & Efthimios Providas & Themistocles M. Rassias (ed.), Mathematical Analysis in Interdisciplinary Research, pages 381-416, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-84721-0_18
    DOI: 10.1007/978-3-030-84721-0_18
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