Representation Variety for the Rank One Affine Group

Ángel González-Prieto (), Marina Logares () and Vicente Muñoz ()
Additional contact information
Ángel González-Prieto: Universidad Complutense de Madrid
Marina Logares: Universidad Complutense de Madrid
Vicente Muñoz: Universidad de Málaga

A chapter in Mathematical Analysis in Interdisciplinary Research, 2021, pp 381-416 from Springer

Abstract: 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.

Date: 2021
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-84721-0_18

Ordering information: This item can be ordered from
http://www.springer.com/9783030847210

DOI: 10.1007/978-3-030-84721-0_18

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().