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Higher Teichmüller theory for surface groups and shifts of finite type
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Pollicott, Mark and Sharp, Richard (2021) Higher Teichmüller theory for surface groups and shifts of finite type. In: Pollicott, M. and Vaienti, S., (eds.) Thermodynamic Formalism. Lecture Notes in Mathematics, 2290 . Cham: Springer, pp. 395-418. ISBN 9783030748623
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Official URL: https://doi.org/10.1007/978-3-030-74863-0_12
Abstract
The Teichmüller space of Riemann metrics on a compact oriented surface V without boundary comes equipped with a natural Riemannian metric called the Weil–Petersson metric. Bridgeman, Canary, Labourie and Sambarino generalised this to Higher Teichmüller Theory, i.e. representations of π1(V ) in SL(d,R) , and showed that their metric is analytic. In this note we will present a new equivalent definition of the Weil–Petersson metric for Higher Teichmüller Theory and also give a short proof of analyticity. Our approach involves coding π1(V ) in terms of a symbolic dynamical system and the associated thermodynamic formalism.
| Item Type: | Book Item | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Teichmèuller spaces, Ergodic theory, Fractals, Riemann surfaces, Lie groups | ||||||
| Series Name: | Lecture Notes in Mathematics | ||||||
| Publisher: | Springer | ||||||
| Place of Publication: | Cham | ||||||
| ISBN: | 9783030748623 | ||||||
| ISSN: | 0075-8434 | ||||||
| Book Title: | Thermodynamic Formalism | ||||||
| Editor: | Pollicott, M. and Vaienti, S. | ||||||
| Official Date: | 22 April 2021 | ||||||
| Dates: |
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| Volume: | 2290 | ||||||
| Page Range: | pp. 395-418 | ||||||
| DOI: | 10.1007/978-3-030-74863-0_12 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Copyright Holders: | © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 | ||||||
| Date of first compliant deposit: | 7 March 2022 |
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