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 , and study its centers. As a consequence, we prove that the set of fixed points is contractible with respect to the Tits topology.
Cite this article
Koji Fujiwara, Koichi Nagano, Takashi Shioya, Fixed point sets of parabolic isometries of CAT(0)-spaces. Comment. Math. Helv. 81 (2006), no. 2, pp. 305–335DOI 10.4171/CMH/54