Proceedings of the American Mathematical Society

Author(s): Igor Nikolaev
Journal: Proc. Amer. Math. Soc. 128 (2000), 1177-1183.
MSC (1991): Primary 46L40, 57R30, 58F10
Posted: October 18, 1999
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Abstract: We introduce a continuous dimension function $\alpha: \bullet\to\mathbb{R}$ on the Grothendieck group

over the crossed product

-algebra $C(X)\rtimes _{\phi}\mathbb{Z}$ . The function $\alpha$ has an elegant geometry: on every minimal flow $\phi^t$ it takes the value of the ``rotation number" of $\phi^t$ ; such a problem was posed in 1936 by A. Weil.

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