Rigidity of diagonally embedded triangle groups

Burelle, Jean-Philippe

doi:10.48550/arxiv.1906.03120

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Appendix a Expected Dimensions Of Hitchin Components2

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“…We will call the latter dimension the expected dimension of the Hitchin component, and we will show here that the two dimensions agree. For triangle groups, J.P. Burelle has studied the expected dimension of non-Hitchin components in [Bur19].…”

Section: Appendix a Expected Dimensions Of Hitchin Componentsmentioning

confidence: 99%

“…However, it may not be true hat the expected dimension is in fact equal to the actual dimension in those cases. In fact, the expected dimension can sometimes be negative ([Bur19]). That is why, in this paper, we do not mention the expected dimensions of components of Hit(π 1 Y, PGL(n, R)) other than the Hitchin component.…”

Section: Appendix a Expected Dimensions Of Hitchin Componentsmentioning

confidence: 99%

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Hitchin components for orbifolds

Alessandrini¹,

Lee²

2018

Preprint

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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.

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Section: Appendix a Expected Dimensions Of Hitchin Componentsmentioning

confidence: 99%

Section: Appendix a Expected Dimensions Of Hitchin Componentsmentioning

confidence: 99%