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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 [1,2] 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
References
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