On the Browder-Levine-Novikov embedding theorems

TL;DR

This survey discusses how complement and neighborhood ideas facilitate the reduction of manifold embedding and isotopy problems into algebraic problems, focusing on the Browder-Levine theorem.

Contribution

It provides a clearer exposition of the Browder-Levine theorem and demonstrates applications of complement and neighborhood concepts in embedding theory.

Findings

Reduction of embeddability problems to algebraic problems

Clarified exposition of the Browder-Levine theorem

Accessible survey for non-specialists

Abstract

In this survey we present applications of the ideas of complement and neighborhood in the theory embeddings of manifolds into Euclidean space (in codimension at least three). We describe how the combination of these ideas gives a reduction of embeddability and isotopy problems to algebraic problems. We present a more clarified exposition of the Browder-Levine theorem on realization of normal systems. Most of the survey is accessible to non-specialists in the theory of embeddings.