Degeneration of Hitchin representations along internal sequences

We first give a coordinate system on the P S L ( n , R ) Hitchin component that is a direct analogue of the Fenchel–Nielsen coordinates on Teichmüller space. Using these coordinates, we consider a class of sequences in the Hitchin component, called internal sequences, along which most length functio...

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Bibliographic Details
Published inGeometric and functional analysis Vol. 25; no. 5; pp. 1588 - 1645
Main Author Zhang, Tengren
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2015
Subjects
Analysis
Mathematics
Mathematics and Statistics
Cross Ratio
Internal Sequence
Combinatorial Description
Topological Entropy
Dimensional Subspace
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Summary:We first give a coordinate system on the P S L ( n , R ) Hitchin component that is a direct analogue of the Fenchel–Nielsen coordinates on Teichmüller space. Using these coordinates, we consider a class of sequences in the Hitchin component, called internal sequences, along which most length functions grow to infinity and the topological entropy of the associated geodesic flow converges to 0.
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-015-0342-7