Lecture (2006) /The 21st Century COE Program /Math of OCU(J)

The 21st Century COE Program

Constitution of wide-angle mathematical basis focused on knots

Department of Mathematics and Physics
Graduate School of Science
Osaka City University

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Lecture (2006)(2005）

COE21 Selected Topics IV

Lecturer	：HAMACHI, Toshihiro (Kyushu University)
Title	：Topological and finitary orbit equivalence
Date	：May 30(Tue.)～June 2(Fri.), 2006
Time	：14：30-16：00　（May 30) 　13：00-15：00　（May 31-June 2）
Place	：Dept. of Mathematics, Sci. Bldg., 3040

Abstracts

Bratteli diagrams have received attention in several mathematical directions, since they were introduced by O.Bratteli for classification of C*-algebras. In topological dynamics, Cantor minimal systems can be　presented using them, and also in a similar way they can represent ergodic probability measure preserving transformations. Through these presentations, one can ask what the nature of Dye's theorem on orbit equivalence becomes. The answers are given by T.Giordano, I.Putnam, and C.Skau in the Cantor minimal case, and by T.Hamachi and M.Keane in the finitary case, dealing with ergodic measure preserving transformations.

Here we discuss an improvement by giving a dynamical proof of the GPS-theorem, which was conjectured (and half of it proved) by E.Glasner and B.Weiss.
This is a joint work with Professors M.Keane (Wesleyan Univ.) and H.Yuasa (Kyushu Univ.).

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