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

  • Koji Fujiwara

    Kyoto University, Japan
  • Koichi Nagano

    Tohoku University, Sendai, Japan
  • Takashi Shioya

    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 π/2\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.

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. 305–335

DOI 10.4171/CMH/54