The Library
Higher Teichmüller theory for surface groups and shifts of finite type
Tools
Tools
Tools
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
|
PDF
WRAP-Higher-Teichmuller-theory-surface-shifts-finite-type-2021.pdf - Accepted Version - Requires a PDF viewer. Download (454Kb) | Preview |
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: |
|
||||||
| 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 | ||||||
| Date of first compliant Open Access: | 22 April 2023 |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
