Spin Borromean surgeries

Massuyeau, Gwénaël

doi:10.1090/S0002-9947-03-03071-X

Spin Borromean surgeries
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Trans. Amer. Math. Soc. 355 (2003), 3991-4017 Request permission

Abstract:

In 1986, Matveev defined the notion of Borromean surgery for closed oriented $3$-manifolds and showed that the equivalence relation generated by this move is characterized by the pair (first Betti number, linking form up to isomorphism).

We explain how this extends for $3$-manifolds with spin structure if we replace the linking form by the quadratic form defined by the spin structure. We then show that the equivalence relation among closed spin $3$-manifolds generated by spin Borromean surgeries is characterized by the triple (first Betti number, linking form up to isomorphism, Rochlin invariant modulo $8$).

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