Borromean surgery equivalence of spin 3-manifolds with boundary

TL;DR

This paper extends the understanding of Borromean surgery equivalence from closed and boundaryless 3-manifolds to include compact, spin 3-manifolds with boundary, broadening the classification framework.

Contribution

It provides a partial generalization of existing results on Borromean surgery equivalence to compact, spin 3-manifolds with boundary.

Findings

Characterization of Borromean surgery equivalence for spin 3-manifolds with boundary

Extension of previous classification results to manifolds with boundary

Partial generalization of the invariants involved in Borromean surgery

Abstract

Matveev introduced Borromean surgery on 3-manifolds, and proved that the equivalence relation on closed, oriented 3-manifolds generated by Borromean surgeries is characterized by the first homology group and the torsion linking pairing. Massuyeau generalized this result to closed, spin 3-manifolds, and the second author to compact, oriented 3-manifolds with boundary. In this paper we give a partial generalization of these results to compact, spin 3-manifolds with boundary.