Representation variety for the rank one affine group

González-Prieto, Ángel and Logares Jiménez, Marina and Muñoz Velázquez, Vicente (2020). Representation variety for the rank one affine group. "Algebraic Geometry (math.AG)" ; pp. 1-28.

Description

Title: Representation variety for the rank one affine group
Author/s:
  • González-Prieto, Ángel
  • Logares Jiménez, Marina
  • Muñoz Velázquez, Vicente
Item Type: Article
Título de Revista/Publicación: Algebraic Geometry (math.AG)
Date: 11 September 2020
Subjects:
Freetext Keywords: TQFT; Moduli spaces; E-polynomial; Representation varieties
Faculty: E.T.S.I. de Sistemas Informáticos (UPM)
Department: Sistemas Informáticos
Creative Commons Licenses: Recognition - No derivative works - Non commercial

Full text

[img]
Preview
PDF - Requires a PDF viewer, such as GSview, Xpdf or Adobe Acrobat Reader
Download (614kB) | Preview

Abstract

The aim of this paper 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.

More information

Item ID: 64351
DC Identifier: https://oa.upm.es/64351/
OAI Identifier: oai:oa.upm.es:64351
Official URL: https://arxiv.org/abs/2005.01841v3
Deposited by: Memoria Investigacion
Deposited on: 19 Jan 2021 10:18
Last Modified: 19 Jan 2021 10:18
  • Logo InvestigaM (UPM)
  • Logo GEOUP4
  • Logo Open Access
  • Open Access
  • Logo Sherpa/Romeo
    Check whether the anglo-saxon journal in which you have published an article allows you to also publish it under open access.
  • Logo Dulcinea
    Check whether the spanish journal in which you have published an article allows you to also publish it under open access.
  • Logo de Recolecta
  • Logo del Observatorio I+D+i UPM
  • Logo de OpenCourseWare UPM