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https://doi.org/10.4171/CMH/461
Title: | Positively ratioed representations | Authors: | Martone, Giuseppe Zhang, Tengren |
Keywords: | Science & Technology Physical Sciences Mathematics Hitchin representations maximal representations higher Teichmiiller theory geodesic currents SURFACE GROUPS HYPERCONVEX REPRESENTATIONS MAXIMAL REPRESENTATIONS ANOSOV REPRESENTATIONS CROSS RATIOS DEGENERATION SPACES COMPONENTS COCYCLES ENTROPY |
Issue Date: | 2019 | Publisher: | EUROPEAN MATHEMATICAL SOC | Citation: | Martone, Giuseppe, Zhang, Tengren (2019). Positively ratioed representations. COMMENTARII MATHEMATICI HELVETICI 94 (2) : 273-345. ScholarBank@NUS Repository. https://doi.org/10.4171/CMH/461 | Abstract: | Let S be a closed orientable surface of genus at least 2 and let G be a semisimple real algebraic group of non-compact type. We consider a class of representations from the fundamental group of S to G called positively ratioed representations. These are Anosov representations with the additional condition that certain associated cross ratios satisfy a positivity property. Examples of such representations include Hitchin representations and maximal representations. Using geodesic currents, we show that the corresponding length functions for these positively ratioed representations are well-behaved. In particular, we prove a systolic inequality that holds for all such positively ratioed representations. | Source Title: | COMMENTARII MATHEMATICI HELVETICI | URI: | https://scholarbank.nus.edu.sg/handle/10635/244743 | ISSN: | 0010-2571 1420-8946 |
DOI: | 10.4171/CMH/461 |
Appears in Collections: | Elements Staff Publications |
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