We prove the Ingram conjecture, ie we show that the inverse limit spaces of tent maps with different slopes in the interval 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.
"The Ingram conjecture." Geom. Topol. 16 (4) 2481 - 2516, 2012. https://doi.org/10.2140/gt.2012.16.2481