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Geometry of a crossed product

Authors:	Igor Nikolaev

Institution:	CRM, Université de Montréal, Montréal H3C 3J7, Canada - Fields Institute, 222 College Stree, Toronto, Canada M5T 3J1

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.

Keywords:	Dimension group continued fraction minimal flow

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