Geodesic
On the Radius of Comparison of a Commutative C*-algebra
Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 737-744

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Let $X$ be a compact metric space. A lower bound for the radius of comparison of the ${{\text{C}}^{*}}$ -algebra $\text{C}\left( X \right)$ is given in terms of ${{\dim}_{\mathbb{Q}}}\,X$ , where ${{\dim}_{\mathbb{Q}}}\,X$ is the cohomological dimension with rational coefficients. If ${{\dim}_{\mathbb{Q}}}\,X\,=\,\dim\,X\,=\,d$ , then the radius of comparison of the ${{\text{C}}^{*}}$ -algebra $C\left( X \right)$ is $\max \left\{ 0,\,\left( d\,-\,1 \right)/\,2\,-\,1 \right\}$ if $d$ is odd, and must be either ${d}/{2}\;\,-\,1$ or ${d}/{2}\;\,-\,2$ if $d$ is even (the possibility ${d}/{2}\;\,-\,1$ does occur, but we do not know if the possibility ${d}/{2}\;\,-\,2$ can also occur).
DOI : 10.4153/CMB-2012-012-9
Mots-clés : 46L80, Cuntz semigroup, comparison radius, cohomology dimension, covering dimension 
Elliott, George A.; Niu, Zhuang. On the Radius of Comparison of a Commutative C*-algebra. Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 737-744. doi: 10.4153/CMB-2012-012-9
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     author = {Elliott, George A. and Niu, Zhuang},
     title = {On the {Radius} of {Comparison} of a {Commutative} {C*-algebra}},
     journal = {Canadian mathematical bulletin},
     pages = {737--744},
     year = {2013},
     volume = {56},
     number = {4},
     doi = {10.4153/CMB-2012-012-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-012-9/}
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