Surfaces, submanifolds, and aligned Fox reimbedding in non-Haken 3-manifolds
Geometric Topology
2007-05-23 v1
Abstract
Understanding non-Haken 3-manifolds is central to many current endeavors in 3-manifold topology. We describe some results for closed orientable surfaces in non-Haken manifolds, and extend Fox's theorem for submanifolds of the 3-sphere to submanifolds of general non-Haken manifolds. In the case where the submanifold has connected boundary, we show also that the boundary-connected sum decomposition of the submanifold can be aligned with such a structure on the submanifold's complement.
Keywords
Cite
@article{arxiv.math/0308011,
title = {Surfaces, submanifolds, and aligned Fox reimbedding in non-Haken 3-manifolds},
author = {Martin Scharlemann and Abigail Thompson},
journal= {arXiv preprint arXiv:math/0308011},
year = {2007}
}
Comments
10 pages