3-manifolds with more than one abelian embedding

TL;DR

This paper constructs specific 3-manifolds that admit multiple inequivalent embeddings with abelian fundamental groups in their complementary regions, highlighting complex embedding behaviors.

Contribution

It introduces a method to construct 3-manifolds with multiple inequivalent abelian embeddings, expanding understanding of embedding diversity.

Findings

Existence of 3-manifolds with multiple abelian embeddings

Construction techniques for such manifolds

Insights into embedding inequivalence

Abstract

We construct 3-manifolds which have at least two inequivalent embeddings such that both complementary regions have abelian fundamental group.