Continuous interval exchange actions

Novak, Christopher F

doi:10.2140/agt.2010.10.1609

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Continuous interval exchange actions

Christopher F Novak

Algebraic & Geometric Topology 10 (2010) 1609–1625

DOI: 10.2140/agt.2010.10.1609

Abstract

Let $ℰ$ denote the group of all interval exchange transformations on $0 \leq x < 1$ Given a suitable topological group structure on $ℰ$ , it is possible to classify all one-parameter interval exchange actions (continuous homomorphisms $ℝ \to ℰ$ ). In particular, up to conjugacy in $ℰ$ , any one-parameter interval exchange action factors through a rotational torus action.

Keywords

interval exchange, group action, one-parameter subgroup

Mathematical Subject Classification 2000

Primary: 37E05, 54H15

Secondary: 57S05, 37A10, 57M60

References

Publication

Received: 20 February 2010

Accepted: 29 April 2010

Published: 21 July 2010

Authors

Christopher F Novak
Department of Mathematics and Statistics The University of Michigan-Dearborn 4901 Evergreen Road Dearborn, MI 48128 USA
http://www-personal.umd.umich.edu/~cfnovak/Site/Homepage.html

Volume 10, issue 3 (2010)