Dimension of representation and character varieties for two- and three-orbifolds

Porti, Joan

doi:10.2140/agt.2022.22.1905

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Dimension of representation and character varieties for two- and three-orbifolds

Joan Porti

Algebraic & Geometric Topology 22 (2022) 1905–1967

DOI: 10.2140/agt.2022.22.1905

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 $SL (n, ℂ)$ .

Keywords

variety of representations, variety of characters, orbifold

Mathematical Subject Classification

Primary: 14D20, 57K32

Secondary: 57K20

References

Publication

Received: 7 September 2020

Revised: 10 March 2021

Accepted: 3 May 2021

Published: 10 October 2022

Authors

Joan Porti
Departament de Matemàtiques Universitat Autònoma de Barcelona Barcelona Spain	Centre de Recerca Matemàtica Barcelona Spain
https://mat.uab.cat/~porti

Volume 22, issue 4 (2022)