Degenerations of k-positive surface group representations

Jonas Beyrer; Beatrice Pozzetti

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arXiv · 2106.05983

Degenerations of k-positive surface group representations

Jonas Beyrer·Beatrice Pozzetti

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Abstract

We introduce \emph{k-positive representations}, a large class of $\{1,\ldots,k\}$--Anosov surface group representations into PGL(E) that share many features with Hitchin representations, and we study their degenerations: unless they are Hitchin, they can be deformed to non-discrete representations, but any limit is at least (k-3)-positive and irreducible limits are (k-1)-positive. A major ingredient, of independent interest, is a general limit theorem for positively ratioed representations.

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Jonas Beyrer, Beatrice Pozzetti. 2021-06-10. Degenerations of k-positive surface group representations. https://arxiv.org/abs/2106.05983

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