## Kyoto Journal of Mathematics

### The coarse Baum–Connes conjecture for Busemann nonpositively curved spaces

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

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

Digital Object Identifier
doi:10.1215/21562261-3445129

Mathematical Reviews number (MathSciNet)
MR3479315

Zentralblatt MATH identifier
1348.58013

#### 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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