# The classification of linked $3$-manifolds in $6$-space

## TL;DR

This paper classifies how pairs of closed, orientable 3-manifolds can be smoothly or piecewise linearly embedded into 6-dimensional space, providing a comprehensive understanding of their isotopy classes.

## Contribution

It offers a complete classification of embeddings of two 3-manifolds into 6-space up to isotopy, extending previous work on manifold embeddings.

## Key findings

- Classification of embedding isotopy classes for pairs of 3-manifolds in 6-space
- Identification of invariants distinguishing embedding classes
- Framework applicable to both smooth and piecewise linear categories

## Abstract

Let $M_1$ and $M_2$ be closed connected orientable $3$-manifolds. We classify the sets of smooth and piecewise linear isotopy classes of embeddings $M_1\sqcup M_2\rightarrow S^6$.