TY - JOUR
T1 - Hitchin components for orbifolds
AU - Alessandrini, Daniele
AU - Lee, Gye Seon
AU - Schaffhauser, Florent
N1 - Publisher Copyright:
© 2023 European Mathematical Society Publishing House. All rights reserved.
PY - 2023
Y1 - 2023
N2 - We extend the notion of Hitchin component from surface groups to orbifold groups and prove that this gives new examples of higher Teichmüller spaces. We show that the Hitchin component of an orbifold group is homeomorphic to an open ball and we compute its dimension explicitly. We then give applications to the study of the pressure metric, cyclic Higgs bundles, and the deformation theory of real projective structures on 3-manifolds.
AB - We extend the notion of Hitchin component from surface groups to orbifold groups and prove that this gives new examples of higher Teichmüller spaces. We show that the Hitchin component of an orbifold group is homeomorphic to an open ball and we compute its dimension explicitly. We then give applications to the study of the pressure metric, cyclic Higgs bundles, and the deformation theory of real projective structures on 3-manifolds.
KW - Coxeter group
KW - Hitchin component
KW - Teichmüller space
KW - orbifold
KW - real projective structure
UR - http://www.scopus.com/inward/record.url?scp=85153868349&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85153868349&partnerID=8YFLogxK
U2 - 10.4171/JEMS/1210
DO - 10.4171/JEMS/1210
M3 - Article
AN - SCOPUS:85153868349
SN - 1435-9855
VL - 25
SP - 1285
EP - 1347
JO - Journal of the European Mathematical Society
JF - Journal of the European Mathematical Society
IS - 4
ER -