A proof of Lickorish and Wallace's theorem

TL;DR

This paper provides a simplified proof of Lickorish and Wallace's theorem, demonstrating that all closed orientable 3-manifolds can be constructed via surgery on links in the 3-sphere.

Contribution

It offers a more straightforward proof of a fundamental theorem in 3-manifold topology, enhancing understanding and accessibility.

Findings

Simplified proof of Lickorish and Wallace's theorem

Every closed orientable 3-manifold can be obtained by surgery on a link in S^3

Improved clarity in the construction of 3-manifolds

Abstract

In this paper, we give a simple proof of Lickorish and Wallace's theorem, which states that every closed orientable 3-manifold is obtained by surgery on some link in 3-sphere.