The Ingram conjecture

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.