The 4-Dimensional Light Bulb Theorem (after David Gabai)

TL;DR

This paper offers an interpretation of David Gabai's smooth proof of the 4-Dimensional Light Bulb Theorem, highlighting its innovative approach in constructive smooth 4-manifold theory.

Contribution

It provides a detailed understanding of Gabai's proof, showcasing a novel smooth construction in 4-manifold topology that is the first of its kind in recent years.

Findings

Gabai's proof is a smooth, constructive approach.

The proof combines classical moves in a novel way.

It represents a significant advance in smooth 4-manifold theory.

Abstract

In this note I present my understanding of, that is to say the way I look at, David Gabai's proof of his recent 4-Dimensional Light Bulb Theorem (4D-LBT). His construction, entirely smooth, is an ingenious amalgam of classical moves, and represents the first new hands-on advance in constructive smooth 4-manifold theory, that I am aware of, in a long time.