English

Open 3-manifolds which are connected sums of closed ones

Differential Geometry 2020-02-03 v1

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.

Keywords

Cite

@article{arxiv.2001.11883,
  title  = {Open 3-manifolds which are connected sums of closed ones},
  author = {Laurent Bessières and Gérard Besson and Sylvain Maillot},
  journal= {arXiv preprint arXiv:2001.11883},
  year   = {2020}
}