Journal article
Heegaard surfaces for certain graphs in compressionbodies
Revista Matemática Complutense, Vol.25(2), pp.511-555
07/2012
DOI: 10.1007/s13163-011-0075-6
Abstract
Let M be a compressionbody containing a properly embedded graph T (with at least one edge) such that ∂ + M−T is parallel to the frontier of T∪∂ − M in M. We extend methods of Hayashi and Shimokawa to show that if H is a bridge surface for T then one of the following occurs: H is stabilized, boundary stabilized, or perturbed. T contains a removable path. M is a trivial compressionbody and H−T is properly isotopic in M−T to ∂ + M−T. The results of this paper are used in later work to show that if a bridge surface for a graph in a 3-manifold is c-weakly reducible then either a degenerate situation occurs or the exterior of the graph contains an essential meridional surface.
Details
- Title: Subtitle
- Heegaard surfaces for certain graphs in compressionbodies
- Creators
- Scott Taylor - Colby College 5832 Mayflower Hill Waterville ME 04901 USAMaggy Tomova - University of Iowa 14 MacLean Hall Iowa City IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Revista Matemática Complutense, Vol.25(2), pp.511-555
- DOI
- 10.1007/s13163-011-0075-6
- ISSN
- 1139-1138
- eISSN
- 1988-2807
- Publisher
- Springer Milan; Milan
- Language
- English
- Date published
- 07/2012
- Academic Unit
- Liberal Arts and Science Admin; Mathematics
- Record Identifier
- 9983985991502771
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