Abstract
AbstractThe famous Haken–Kneser–Milnor theorem states that every 3-manifold can be expressed in a unique way as a connected sum of prime 3-manifolds. The analogous statement for 3-orbifolds has been part of the folklore for several years, and it was commonly believed that slight variations on the argument used for manifolds would be sufficient to establish it. We demonstrate in this paper that this is not the case, proving that the apparently natural notion of “essential” system of spherical 2-orbifolds is not adequate in this context. We also show that the statement itself of the theorem must be given in a substantially different way. We then prove the theorem in full detail, using a certain notion of “efficient splitting system.”
Publisher
Cambridge University Press (CUP)
Cited by
10 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Equivariant Heegaard genus of reducible 3-manifolds;Mathematical Proceedings of the Cambridge Philosophical Society;2023-02-13
2. Classification of non-free Kleinian groups generated by two parabolic transformations;Transactions of the American Mathematical Society;2021-01-12
3. Fixed-point free circle actions on 4–manifolds;Algebraic & Geometric Topology;2015-12-31
4. Guts of Surfaces and the Colored Jones Polynomial;Lecture Notes in Mathematics;2013
5. Ideal Polyhedra;Lecture Notes in Mathematics;2012-10-04