Heegaard surfaces for certain graphs in compressionbodies

Scott A. Taylor; Maggy Tomova

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arXiv · 0910.3019

Heegaard surfaces for certain graphs in compressionbodies

Scott A. Taylor·Maggy Tomova

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Abstract

Let M be a compressionbody containing a graph T (with at least one edge) such that \boundary_+ M is parallel to the union of T and \boundary_- M. We extend methods of Hayashi and Shimokawa to classify bridge surfaces for 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.

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Scott A. Taylor, Maggy Tomova. 2009-12-21. Heegaard surfaces for certain graphs in compressionbodies. https://arxiv.org/abs/0910.3019

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