Topological groups with rokhlin properties

Eli Glasner; Benjamin Weiss

doi:10.4064/cm110-1-2

Topological groups with rokhlin properties

Eli Glasner
, Benjamin Weiss

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

In his classical paper [Ann. of Math. 45 (1944)] P. R. Halmos shows that weak mixing is generic in the measure preserving transformations. Later, in his book, Lectures on Ergodic Theory, he gave a more streamlined proof of this fact based on a fundamental lemma due to V. A. Rokhlin. For this reason the name of Rokhlin has been attached to a variety of results, old and new, relating to the density of conjugacy classes in topological groups. In this paper we will survey some of the new developments in this area.

Original language	English
Pages (from-to)	51-80
Number of pages	30
Journal	Colloquium Mathematicum
Volume	110
Issue number	1
DOIs	https://doi.org/10.4064/cm110-1-2
State	Published - 2008

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN, 2008.

Keywords

Cantor group
Dense conjugacy class
Fraïssé structure
Group of homeomorphisms
Measure preserving transformation
Rokhlin property
Weak mixing

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abstract = "In his classical paper [Ann. of Math. 45 (1944)] P. R. Halmos shows that weak mixing is generic in the measure preserving transformations. Later, in his book, Lectures on Ergodic Theory, he gave a more streamlined proof of this fact based on a fundamental lemma due to V. A. Rokhlin. For this reason the name of Rokhlin has been attached to a variety of results, old and new, relating to the density of conjugacy classes in topological groups. In this paper we will survey some of the new developments in this area.",

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N2 - In his classical paper [Ann. of Math. 45 (1944)] P. R. Halmos shows that weak mixing is generic in the measure preserving transformations. Later, in his book, Lectures on Ergodic Theory, he gave a more streamlined proof of this fact based on a fundamental lemma due to V. A. Rokhlin. For this reason the name of Rokhlin has been attached to a variety of results, old and new, relating to the density of conjugacy classes in topological groups. In this paper we will survey some of the new developments in this area.

AB - In his classical paper [Ann. of Math. 45 (1944)] P. R. Halmos shows that weak mixing is generic in the measure preserving transformations. Later, in his book, Lectures on Ergodic Theory, he gave a more streamlined proof of this fact based on a fundamental lemma due to V. A. Rokhlin. For this reason the name of Rokhlin has been attached to a variety of results, old and new, relating to the density of conjugacy classes in topological groups. In this paper we will survey some of the new developments in this area.

KW - Cantor group

KW - Dense conjugacy class

KW - Fraïssé structure

KW - Group of homeomorphisms

KW - Measure preserving transformation

KW - Rokhlin property

KW - Weak mixing

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JO - Colloquium Mathematicum

JF - Colloquium Mathematicum

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ER -

Topological groups with rokhlin properties

Abstract

Bibliographical note

Keywords

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