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 σ̂^N switch composants in the same way, where σ̂ is the standard shift map of the inverse limit space.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm207-3-2,
author = {Stewart Baldwin},
title = {Inverse limits of tentlike maps on trees},
journal = {Fundamenta Mathematicae},
volume = {209},
year = {2010},
pages = {211-254},
zbl = {1192.54012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm207-3-2}
}
Stewart Baldwin. Inverse limits of tentlike maps on trees. Fundamenta Mathematicae, Tome 209 (2010) pp. 211-254. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm207-3-2/