# Symplectomorphisms of exotic discs

## TL;DR

This paper constructs a symplectic structure on a disc with an exotic symplectomorphism that cannot be smoothly isotoped to the identity, introducing new techniques involving overtwisted ends and a symplectic Gromoll filtration.

## Contribution

It introduces a novel symplectic structure on a disc with an exotic symplectomorphism and develops a symplectic analogue of the Gromoll filtration.

## Key findings

- Existence of a symplectic structure with an exotic symplectomorphism
- Development of a symplectic Gromoll filtration
- Construction based on a unitary Milnor-Munkres pairing

## Abstract

We construct a symplectic structure on a disc that admits a compactly supported symplectomorphism which is not smoothly isotopic to the identity. The symplectic structure has an overtwisted concave end; the construction of the symplectomorphism is based on a unitary version of the Milnor-Munkres pairing. En route, we introduce a symplectic analogue of the Gromoll filtration.