Simple geodesics and Markoff quads

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Authors
Huang, Y; Norbury, P
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Date
2017-02-01
Source Title
Geometriae Dedicata
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Publisher
Springer
Melbourne Authors
Norbury, Paul ORCID
 HUANG, YI
Affiliation
School of Mathematics and Statistics
Document Type
Journal Article
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Citation
Huang, Y. & Norbury, P. (2017). Simple geodesics and Markoff quads. Geometriae Dedicata, 186 (1), pp.113-148. https://doi.org/10.1007/s10711-016-0182-0.
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Open Access
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https://hdl.handle.net/11343/282712
DOI
10.1007/s10711-016-0182-0
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Open Access at PMC
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ARC/DP1094328
Description
Abstract
The action of the mapping class group of the thrice-punctured projective plane on its GL(2,C) character variety produces an algorithm for generating the simple length spectra of quasi-Fuchsian thrice-punctured projective planes. We apply this algorithm to quasi-Fuchsian representations of the corresponding fundamental group to prove: a sharp upper-bound for the length its shortest geodesic, a McShane identity and the surprising result of non-polynomial growth for the number of simple closed geodesic lengths.
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https://doi.org/10.1007/s10711-016-0182-0
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School of Mathematics and Statistics - Research Publications
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