2003/08/01 by Martin Scharlemann, Scharlemann, Martin, Abigail Thompson +1
Mathematics · #57M25 #57M40 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25 #msc:57M40
paper · pdf · doi:10.48550/arxiv.math/0308011
10 pages
arxiv created 2003/08/01 · arxiv updated 2009/12/01
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.