Spin Borromean surgeries

Gwenael Massuyeau

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arXiv · math/0104065

Spin Borromean surgeries

Gwenael Massuyeau

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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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BibTeX RIS

Gwenael Massuyeau. 2003-01-06. Spin Borromean surgeries. https://arxiv.org/abs/math/0104065

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