Anosov diffeomorphisms constructed from $\pi_k(Diff(S^n))$

TL;DR

This paper constructs Anosov diffeomorphisms on manifolds with exotic smooth structures derived from infranilmanifolds, expanding the understanding of dynamical systems on such complex manifolds.

Contribution

It introduces a method to produce Anosov diffeomorphisms on manifolds with exotic smooth structures obtained via connected sums with exotic spheres.

Findings

Existence of Anosov diffeomorphisms on exotic infranilmanifolds

Construction method applicable to high codimension cases

Manifolds with irreducible exotic smooth structures

Abstract

We construct Anosov diffeomorphisms on manifolds that are homeomorphic to infranilmanifolds yet have exotic smooth structures. These manifolds are obtained from standard infranilmanifolds by connected summing with certain exotic spheres. Our construction produces Anosov diffeomorphisms of high codimension on infranilmanifolds with irreducible exotic smooth structures.