English

Heegaard surfaces for certain graphs in compressionbodies

Geometric Topology 2009-12-21 v2

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.

Keywords

Cite

@article{arxiv.0910.3019,
  title  = {Heegaard surfaces for certain graphs in compressionbodies},
  author = {Scott A. Taylor and Maggy Tomova},
  journal= {arXiv preprint arXiv:0910.3019},
  year   = {2009}
}

Comments

53 pages, 26 figures. Improved Main Theorem in v2

R2 v1 2026-06-21T13:59:02.433Z