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Spin Borromean surgeries

Author(s): Gwénaël Massuyeau
Journal: Trans. Amer. Math. Soc. 355 (2003), 3991-4017.
MSC (2000): Primary 57M27; Secondary 57R15
Posted: June 24, 2003
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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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Additional Information:

Gwénaël Massuyeau
Affiliation: Laboratoire Jean Leray, UMR 6629 CNRS/Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 03, France
Email: massuyea@math.univ-nantes.fr

DOI: 10.1090/S0002-9947-03-03071-X
PII: S 0002-9947(03)03071-X
Keywords: 3-manifolds, finite type invariants, spin structures, $Y$-graphs
Received by editor(s): April 16, 2001
Received by editor(s) in revised form: April 2, 2002
Posted: June 24, 2003
Additional Notes: Commutative diagrams were drawn with Paul Taylor's package
Copyright of article: Copyright 2003, American Mathematical Society

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