Open 3-manifolds which are connected sums of closed ones

Laurent Bessières (1) , Gérard Besson (2) , Sylvain Maillot (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 IF - Institut Fourier
3 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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 Kerékjártó-Richards classification theorem for open surfaces.

Domaines: Géométrie différentielle [math.DG]

Laurent Bessières, Gérard Besson, Sylvain Maillot. Open 3-manifolds which are connected sums of closed ones. 2020. ⟨hal-02462552⟩