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arXiv · 2001.11883

Open 3-manifolds which are connected sums of closed ones

Laurent Bessières·Gérard Besson·Sylvain Maillot
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Abstract

We consider open, oriented 3-manifolds which are infinite connected sums of closed 3-manifolds. We introduce some topological invariants for these manifolds and obtain a classification in the case where there are only finitely many summands up to diffeomorphism. This result encompasses both the Kneser-Milnor Prime Decomposition Theorem for closed 3-manifolds and the Ker{\'e}kj{\'a}rt{\'o}-Richards classification theorem for open surfaces.

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Laurent Bessières, Gérard Besson, Sylvain Maillot. 2020-01-31. Open 3-manifolds which are connected sums of closed ones. https://arxiv.org/abs/2001.11883

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