Inverse limits of tentlike maps on trees

Stewart Baldwin¹

¹ Department of Mathematics and Statistics Auburn University Auburn, AL 36849-5310, U.S.A.

Fundamenta Mathematicae, Tome 207 (2010) no. 3, pp. 211-254

Résumé

We investigate generalizations of Ingram's Conjecture involving maps on trees. We show that for a class of tentlike maps on the $k$-star with periodic critical orbit, different maps in the class have distinct inverse limit spaces. We do this by showing that such maps satisfy the conclusion of the Pseudo-isotopy Conjecture, i.e., if $h$ is a homeomorphism of the inverse limit space, then there is an integer $N$ such that $h$ and $\widehat\sigma^N$ switch composants in the same way, where $\widehat\sigma$ is the standard shift map of the inverse limit space.

Détail

DOI : 10.4064/fm207-3-2

Keywords: investigate generalizations ingrams conjecture involving maps trees class tentlike maps k star periodic critical orbit different maps class have distinct inverse limit spaces showing maps satisfy conclusion pseudo isotopy conjecture homeomorphism inverse limit space there integer widehat sigma switch composants where widehat sigma standard shift map inverse limit space