The Ingram Conjecture

Abstract

We prove the Ingram Conjecture, i.e., we show that the inverse limit spaces of every two tent maps with different slopes in the interval [1, 2] are non-homeomorphic. Based on the structure obtained from the proof, we also show that every self-homeomorphism of the inverse limit space of the tent map is pseudo-isotopic, on the core, to some power of the shift homeomorphism.

Cited by in corpus (6)

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• Natural extensions of unimodal maps: virtual sphere homeomorphisms and prime ends of basin boundaries
• Itineraries for Inverse Limits of Tent Maps: a Backward View
• Entropy of homeomorphisms on unimodal inverse limit spaces
• Planar embeddings of chainable continua
• Unimodal Measurable Pseudo-Anosov Maps