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arXiv · 1806.07020

Ping-pong in Hadamard manifolds

Subhadip Dey·Michael Kapovich·Beibei Liu
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Abstract

In this paper, we prove a quantitative version of the Tits alternative for negatively pinched manifolds $X$. Precisely, we prove that a nonelementary discrete isometry subgroup of $\mathrm{Isom}(X)$ generated by two non-elliptic isometries $g$, $f$ contains a free subgroup of rank $2$ generated by isometries $f^N , h$ of uniformly bounded word length. Furthermore, we show that this free subgroup is convex-cocompact when $f$ is hyperbolic.

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BibTeXRIS

Subhadip Dey, Michael Kapovich, Beibei Liu. 2018-06-19. Ping-pong in Hadamard manifolds. https://doi.org/10.17879/53149722954

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