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

Koji Fujiwara; Koichi Nagano; Takashi Shioya

doi:10.4171/CMH/54

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

Koji Fujiwara, Koichi Nagano, Takashi Shioya

理学研究科・数学専攻

研究成果: Article › 査読

23 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ（範囲）	305-335
ページ数	31
ジャーナル	Commentarii Mathematici Helvetici
巻	81
号	2
DOI	https://doi.org/10.4171/CMH/54
出版ステータス	Published - 2006

ASJC Scopus subject areas

数学 (全般)

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AU - Shioya, Takashi

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AB - 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.

KW - CAT(κ)-space

KW - Ideal boundary

KW - Parabolic isometry

KW - Tits metric

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

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