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}
}