Exotic iterated Dehn twists

TL;DR

This paper investigates automorphisms of cotangent bundles of exotic spheres, showing that certain symplectic automorphisms analogous to Dehn twists have infinite order up to isotopy, revealing new insights into their symplectic mapping class groups.

Contribution

It introduces and analyzes automorphisms of cotangent bundles of exotic spheres that are analogous to Dehn twists, proving they have infinite order up to isotopy.

Findings

Automorphisms preserve the behavior at infinity of a fiber.

Such automorphisms are of infinite order up to isotopy.

The work extends understanding of symplectic automorphisms of exotic spheres.

Abstract

Consider cotangent bundles of exotic spheres, with their canonical symplectic structure. They admit automorphisms which preserve the part at infinity of one fibre, and which are analogous to the square of a Dehn twist. Pursuing that analogy, we show that they have infinite order up to isotopy (inside the group of all automorphisms with the same behaviour).