On isotopy of self-homeomorphisms of quadratic inverse limit spaces

TL;DR

This paper proves that all self-homeomorphisms of quadratic inverse limit spaces are isotopic to powers of the shift map, revealing a fundamental symmetry in these complex topological structures.

Contribution

It establishes a complete classification of self-homeomorphisms in quadratic inverse limit spaces up to isotopy, a significant advancement in topological dynamics.

Findings

Every self-homeomorphism is isotopic to a shift power

The structure of quadratic inverse limit spaces is highly symmetric

Classification simplifies understanding of these spaces

Abstract

We prove that every self-homeomorphism on the inverse limit space of a quadratic map is isotopic to some power of the shift map.