Extending maps of a Cantor set product with an arc to near homeomorphisms of the 2-disk

Michael D. Sanford and Russell B. Walker

Vol. 192 (2000), No. 2, 369–384

DOI: 10.2140/pjm.2000.192.369

Abstract

We prove that a positive entropy map of the product of a Cantor Set and an arc (which covers a homeomorphism) cannot be “embedded” into a near homeomorphism of the 2-disk. Thus a theorem of M. Brown cannot be used to embed the induced shift map on the corresponding inverse limit space into a 2-disk homeomorphism.

Milestones

Received: 18 July 1996

Revised: 16 December 1996

Published: 1 February 2000