Infinite order corks via handle diagrams

Robert E. Gompf

Published 2016-07-15Version 1

The author recently proved the existence of infinite order corks, arXiv:1603.05090. The present paper exhibits the first handle diagrams of this phenomenon, by translating the earlier proof into this language. Preliminary notes for this work also provided key diagrams for Akbulut's recent posting arXiv:1605.09348. While that paper provides a different viewpoint, we show that at a fundamental level the technique is equivalent, and the proof sketched in that paper is a special case of the author's diagrammatic translation of the original. The cork twists defined in the author's original paper and drawn in the subsequent papers are twists on incompressible tori. We give conditions guaranteeing that such twists do not change the diffeomorphism type of a 4-manifold, partially answering a question from the original paper.