Modeling complex points up to isotopy

TL;DR

This paper classifies complex points of real 4-manifolds embedded in complex 3-manifolds up to isotopy, showing only two types exist and that such embeddings can be isotoped to have 2-complete neighborhoods.

Contribution

It establishes a classification of complex points up to isotopy and demonstrates the possibility of deforming embeddings to achieve 2-complete neighborhoods.

Findings

Only two types of complex points exist up to isotopy.

Any embedding can be isotoped to have a 2-complete neighborhood basis.

Abstract

In this paper we examine the structure of complex points of real 4-manifolds embedded into complex 3-manifolds up to isotopy. We show that there are only two types of complex points up to isotopy and as a consequence, show that any such embedding can be deformed by isotopy to a manifold having 2-complete neighborhood basis.