Realizing isomorphisms between first homology groups of closed 3-manifolds by borromean surgeries

Delphine Moussard

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arXiv · 1412.4627

Realizing isomorphisms between first homology groups of closed 3-manifolds by borromean surgeries

Delphine Moussard

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Abstract

We refine Matveev's result asserting that any two closed oriented 3-manifolds can be related by a sequence of borromean surgeries if and only if they have isomorphic first homology groups and linking pairings. Indeed, a borromean surgery induces a canonical isomorphism between the first homology groups of the involved 3-manifolds, which preserves the linking pairing. We prove that any such isomorphism is induced by a sequence of borromean surgeries. As an intermediate result, we prove that a given algebraic square finite presentation of the first homology group of a 3-manifold, which encodes the linking pairing, can always be obtained from a surgery presentation of the manifold.

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Delphine Moussard. 2014-12-15. Realizing isomorphisms between first homology groups of closed 3-manifolds by borromean surgeries. https://arxiv.org/abs/1412.4627

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