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

Koji Fujiwara | Zendy; Koichi Nagano | Zendy; Takashi Shioya | Zendy

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

Author(s) -

Koji Fujiwara,

Koichi Nagano,

Takashi Shioya

Publication year - 2006

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.4171/cmh/54

Subject(s) - mathematics , contractible space , fixed point , isometry (riemannian geometry) , fixed point property , boundary (topology) , set (abstract data type) , pure mathematics , ideal (ethics) , topology (electrical circuits) , mathematical analysis , combinatorics , computer science , programming language , philosophy , epistemology

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 $\pi/2$, and study its centers. As a consequence, we prove that the set of fixed points is contractible with respect to the Tits topology.

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