Dehn surgery and Seifert surface system

TL;DR

This paper explores the relationship between Seifert surface systems in 3-manifolds and Dehn surgeries along null-homologous links, leading to a refined understanding of Fox's re-embedding theorem.

Contribution

It establishes a connection between Seifert surface systems and Dehn surgeries, providing a new perspective and refinement of Fox's re-embedding theorem.

Findings

Relates Seifert surface systems to Dehn surgery along null-homologous links.

Refines Fox's re-embedding theorem.

Provides new tools for understanding 3-manifold embeddings.

Abstract

For a compact connected 3-submanifold with connected boundary in the 3-sphere, we relate the existence of a Seifert surface system for a surface with a Dehn surgery along a null-homologous link. As its corollary, we obtain a refinement of the Fox's re-embedding theorem.