Abstract
Let be a real closed field. We define the notion of a maximal framing for a representation of the fundamental group of a surface with values in . We show that ultralimits of maximal representations in admit such a framing, and that all maximal framed representations satisfy a suitable generalization of the classical collar lemma. In particular, this establishes a collar lemma for all maximal representations into . We then describe a procedure to get from representations in interesting actions on affine buildings, and in the case of representations admitting a maximal framing, we describe the structure of the elements of the group acting with zero translation length.
Citation
Marc Burger. Maria Beatrice Pozzetti. "Maximal representations, non-Archimedean Siegel spaces, and buildings." Geom. Topol. 21 (6) 3539 - 3599, 2017. https://doi.org/10.2140/gt.2017.21.3539
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