Kyoto Journal of Mathematics

The coarse Baum–Connes conjecture for Busemann nonpositively curved spaces

Tomohiro Fukaya and Shin-ichi Oguni

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We prove that the coarse assembly maps for proper metric spaces that are nonpositively curved in the sense of Busemann are isomorphisms, where we do not assume that the spaces have bounded coarse geometry. Also it is shown that we can calculate the coarse K-homology and the K-theory of the Roe algebra by using the visual boundaries.

Article information

Kyoto J. Math., Volume 56, Number 1 (2016), 1-12.

Received: 14 October 2014
Revised: 16 October 2014
Accepted: 16 October 2014
First available in Project Euclid: 15 March 2016

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Zentralblatt MATH identifier

Primary: 58J22: Exotic index theories [See also 19K56, 46L05, 46L10, 46L80, 46M20]

Coarse Baum–Connes conjecture coarse compactification Busemann nonpositively curved space $\operatorname{CAT} (0)$-space visual boundary


Fukaya, Tomohiro; Oguni, Shin-ichi. The coarse Baum–Connes conjecture for Busemann nonpositively curved spaces. Kyoto J. Math. 56 (2016), no. 1, 1--12. doi:10.1215/21562261-3445129.

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