Eliashberg's proof of Cerf's theorem

TL;DR

This paper proves Cerf's theorem that any diffeomorphism of the 3-sphere extends over the 4-ball, using a moduli-theoretic approach based on Eliashberg's filling-with-holomorphic-discs method.

Contribution

It introduces a moduli-theoretic framework to extend Eliashberg's method for proving Cerf's theorem, advancing the understanding of 3- and 4-dimensional topology.

Findings

Proof that any diffeomorphism of the 3-sphere extends over the 4-ball

Development of a moduli-theoretic version of Eliashberg's method

Application of holomorphic discs to topological extension problems

Abstract

Following a line of reasoning suggested by Eliashberg, we prove Cerf's theorem that any diffeomorphism of the 3-sphere extends over the 4-ball. To this end we develop a moduli-theoretic version of Eliashberg's filling-with-holomorphic-discs method.