The Ingram Conjecture

Abstract

We prove the Ingram Conjecture, i.e., we show that the inverse limit spaces of ev- ery two tent maps with di®erent 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.