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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 $n$-componentlink in $Y$ and surgery slopes for that link such that performing Dehn surgeryalong any nonempty sublink yields $Z$. We characterize adjacencies fromthree-manifolds to the three-sphere, providing an analogy to Askitas andKalfagianni's results on $n$-adjacency in knots.

Adjacency of three-manifolds and Brunnian links