Adjacency of three-manifolds and Brunnian links

TL;DR

This paper introduces the concept of adjacency between three-manifolds via Dehn surgery on links, characterizes adjacency to the three-sphere, and draws analogies to knot adjacency results.

Contribution

It defines the notion of adjacency for three-manifolds and characterizes when a three-manifold is adjacent to the three-sphere, extending ideas from knot theory.

Findings

Defined n-adjacency for three-manifolds.

Characterized adjacency to the three-sphere.

Established analogies with knot adjacency results.

Abstract

We introduce the notion of adjacency in three-manifolds. A three-manifold $Y$ is $n$-adjacent to another three-manifold $Z$ if there exists an $n$-component link in $Y$ and surgery slopes for that link such that performing Dehn surgery along any nonempty sublink yields $Z$. We characterize adjacencies from three-manifolds to the three-sphere, providing an analogy to Askitas and Kalfagianni's results on $n$-adjacency in knots.