On an infinite order cork automorphisms

TL;DR

This paper provides a detailed description of an infinite order cork automorphism, constructed through an infinite boundary isotopy, contributing to the understanding of corks in 4-manifold topology.

Contribution

It offers a concrete construction of an infinite order cork automorphism using an explicit boundary isotopy, advancing the study of corks in topology.

Findings

Explicit description of the infinite order cork automorphism.

Construction via concatenation of ribbon disk and infinite isotopy.

Enhanced understanding of cork automorphisms in 4-manifold topology.

Abstract

Here we give a concrete description of the cork automorphism $f:\partial W\to \partial W$ of the infinite order loose-cork $(W,f)$, defined in \cite{a2}. It is obtained by concatenating the defining ribbon disk of $W$ in $B^4$ by an infinite order isotopy of the boundary knot.