Journal article
C-essential surfaces in (3-manifold, graph) pairs
Communications in analysis and geometry, Vol.21(2), pp.295-330
10/16/2009
DOI: 10.4310/CAG.2013.v21.n2.a2
Abstract
Let $T$ be a graph in a compact, orientable 3--manifold $M$ and let $\Gamma$ be a subgraph. $T$ can be placed in bridge position with respect to a Heegaard surface $H$. We show that if $H$ is what we call $(T,\Gamma)$-c-weakly reducible in the complement of $T$ then either a "degenerate" situation occurs or $H$ can be untelescoped and consolidated into a collection of "thick surfaces" and "thin surfaces". The thin surfaces are c-essential (c-incompressible and essential) in the graph exterior and each thick surface is a strongly irreducible bridge surface in the complement of the thin surfaces. This strengthens and extends previous results of Hayashi-Shimokawa and Tomova to graphs in 3-manifolds that may have non-empty boundary.
Details
- Title: Subtitle
- C-essential surfaces in (3-manifold, graph) pairs
- Creators
- Scott TaylorMaggy Tomova
- Resource Type
- Journal article
- Publication Details
- Communications in analysis and geometry, Vol.21(2), pp.295-330
- DOI
- 10.4310/CAG.2013.v21.n2.a2
- ISSN
- 1019-8385
- eISSN
- 1944-9992
- Language
- English
- Date published
- 10/16/2009
- Academic Unit
- Liberal Arts and Science Admin; Mathematics
- Record Identifier
- 9983985862302771
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