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

Koji Fujiwara; Koichi Nagano; Takashi Shioya

doi:10.4171/cmh/54

JournalscmhVol. 81, No. 2pp. 305–335

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

Koji Fujiwara
Kyoto University, Japan
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Koichi Nagano
Tohoku University, Sendai, Japan
- MathSciNet
- zbMATH Open
Takashi Shioya
Tohoku University, Sendai, Japan
- MathSciNet
- zbMATH Open

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Abstract

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 $π /2$ , 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