Kyoto Journal of Mathematics

The coarse Baum–Connes conjecture for Busemann nonpositively curved spaces

Tomohiro Fukaya and Shin-ichi Oguni

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1458047875

Digital Object Identifier
doi:10.1215/21562261-3445129

Mathematical Reviews number (MathSciNet)
MR3479315

Zentralblatt MATH identifier
1348.58013

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

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

Citation

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. https://projecteuclid.org/euclid.kjm/1458047875


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References

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