Dimension of representation and character varieties for two- and three- orbifolds
Porti, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2022
Abstract:	We consider varieties of representations and characters of 2 and 3 dimensional orbifolds in semisimple Lie groups, and we focus on computing their dimension. For hyperbolic 3 orbifolds, we consider the component of the variety of characters that contains the holonomy composed with the principal representation, and show that its dimension equals half the dimension of the variety of characters of the boundary. We also show that this is a lower bound for the dimension of generic components. We furthermore provide tools for computing dimensions of varieties of characters of 2 orbifolds, including the Hitchin component. We apply this computation to the dimension growth of varieties of characters of some 3 dimensional manifolds in SL (n, C).
Grants:	Agencia Estatal de Investigación PGC2018-095998-B-I00
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Orbifold ; Variety of characters ; Variety of representations
Published in:	Algebraic and Geometric Topology, Vol. 22, Issue 4 (2022) , p. 1905-1967, ISSN 1472-2739

DOI: 10.2140/agt.2022.22.1905

Postprint 48 p, 688.6 KB

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