Commentarii Mathematici Helvetici


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Volume 81, Issue 2, 2006, pp. 305–335
DOI: 10.4171/CMH/54

Published online: 2006-06-30

Fixed point sets of parabolic isometries of CAT(0)-spaces

Koji Fujiwara[1], Koichi Nagano[2] and Takashi Shioya[3]

(1) Kyoto University, Japan
(2) Tohoku University, Sendai, Japan
(3) Tohoku University, Sendai, Japan

We study the fixed point set in the ideal boundary of a parabolic isometry of a proper CAT(0)-space. We show that the radius of the fixed point set is at most $\pi/2$, and study its centers. As a consequence, we prove that the set of fixed points is contractible with respect to the Tits topology.

Keywords: CAT(\kappa)-space, ideal boundary, Tits metric, parabolic isometry

Fujiwara Koji, Nagano Koichi, Shioya Takashi: Fixed point sets of parabolic isometries of CAT(0)-spaces. Comment. Math. Helv. 81 (2006), 305-335. doi: 10.4171/CMH/54