Atlas: A Partial Classification of Inverse Limit Spaces of Tent Maps with Periodic Critical Points by Lois Kailhofer

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1999 Spring Topology Conference
March 18-20, 1999
University of Utah
Salt Lake City, UT, USA

Organizers
Mladen Bestvina, Greg Conner, Misha Kapovich, Bruce Kleiner

A Partial Classification of Inverse Limit Spaces of Tent Maps with Periodic Critical Points
by
Lois Kailhofer
University of Wisconsin at Milwaukee

We work within the one parameter family of symmetric tent maps, where the slope is the parameter. Given two such maps f_a, f_b with periodic turning points of the same period, we use the finite kneading sequences of the maps to obtain a necessary condition for the inverse limit spaces (I, f_a) and (I, f_b) to be homeomorphic. As this condition depends only on the parity of the kneading sequences, it is easily checked. To obtain our result, we define topological substructures of a composant, called "wrapping points" and "gaps", and identify properties of these substructures preserved under a homeomorphism. It is known that if the periods differ, then the inverse limit spaces are not homeomorphic.

Date received: January 19, 1999