Inverse limits of the form (I, f) with f in the tent family
by
James Keesling
University of Florida
Coauthors: Louis Block, Slagjana Jakimovik, Lois Kailhofer

Let f_s be a member of the tent family with 1 < s < 2. Let (I, f_s) be the inverse limit of the system {I, f_i} where each f_i is the same tent map f_s. Ingram asked the following question. If (I, f_s) is homeomorphic to (I, f_t), is s = t? There is a partial answer to this question. If the critical points of f_s and of f_t are periodic, then s = t. This was proved by Kailhofer in two papers [Top Appl 123 (2002), 235-265] and [Fund. Math. 177 (2003), 95-120].

In the present talk we present a new proof of this theorem. The new proof also shows that certain homeomorphisms of (I, f_s) are isotopic to powers of the shift map. We will also show how the new proof suggests an approach to answering the general question posed by Ingram.

Date received: February 28, 2005