#### Volume 16, issue 4 (2012)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
The Ingram conjecture

### Marcy Barge, Henk Bruin and Sonja Štimac

Geometry & Topology 16 (2012) 2481–2516
##### Abstract

We prove the Ingram conjecture, ie we show that the inverse limit spaces of tent maps with different slopes in the interval $\left[1,2\right]$ are nonhomeomorphic. Based on the structure obtained from the proof, we also show that every self-homeomorphism of the inverse limit space of a tent map is pseudo-isotopic, on the core, to some power of the shift homeomorphism.

##### Keywords
tent map, inverse limit space, unimodal map, classification, pseudo-isotopy
##### Mathematical Subject Classification 2010
Primary: 54H20
Secondary: 37B45, 37E05
##### Publication
Received: 7 June 2012
Accepted: 14 August 2012
Published: 5 February 2013
Proposed: David Gabai
Seconded: Leonid Polterovich, Steve Ferry
##### Authors
 Marcy Barge Department of Mathematical Sciences Montana State University Bozeman, MT 59717 USA http://www.math.montana.edu/~umsfmbar/ Henk Bruin Faculty of Mathematics University of Vienna Nordbergstrasse 15 1090 Wien Austria http://www.mat.univie.ac.at/~bruin/ Sonja Štimac Department of Mathematics University of Zagreb Bijenička 30 10000 Zagreb Croatia http://www.math.hr/~sonja