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

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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 $\left[1,2\right]$ 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