Freedman, Michael; Howards, Hugh; Wu, Ying-Qing Extension of incompressible surfaces on the boundaries of 3-manifolds. (English) Zbl 1015.57010 Pac. J. Math. 194, No. 2, 335-348 (2000). Summary: An incompressible bounded surface \(F\) on the boundary of a compact, connected, orientable 3-manifold \(M\) is arc-extendible if there is a properly embedded arc \(\gamma\) on \(\partial M-\text{Int} F\) such that \(F\cup N(\gamma)\) is incompressible, where \(N(\gamma)\) is a regular neighborhood of \(\gamma\) in \(\partial M\). Suppose for simplicity that \(M\) is irreducible and \(F\) has no disk components. If \(M\) is a product \(F\times I\), or if \(\partial M-F\) is a set of annuli, then clearly \(F\) is not arc-extendible. The main theorem of this paper shows that these are the only obstructions for \(F\) to be arc-extendible. Cited in 2 Documents MSC: 57N10 Topology of general \(3\)-manifolds (MSC2010) Keywords:incompressible bounded surface; arc-extendible PDFBibTeX XMLCite \textit{M. Freedman} et al., Pac. J. Math. 194, No. 2, 335--348 (2000; Zbl 1015.57010) Full Text: DOI arXiv