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

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

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.

Original language	English
Pages (from-to)	305-335
Number of pages	31
Journal	Commentarii Mathematici Helvetici
Volume	81
Issue number	2
DOIs	https://doi.org/10.4171/CMH/54
Publication status	Published - 2006

Keywords

CAT(κ)-space
Ideal boundary
Parabolic isometry
Tits metric

ASJC Scopus subject areas

Mathematics(all)

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10.4171/CMH/54

Cite this

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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.",

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AU - Nagano, Koichi

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

Abstract

Keywords

ASJC Scopus subject areas

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