Work

C–essential surfaces in (3-manifold, graph) pairs

Year: 2013

Type: article

Abstract: Let T be a graph in a compact, orientable 3-manifold M and let Γ 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, Γ)-cweakly 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.

Source: Communications in Analysis and Geometry

DOI: 10.4310/cag.2013.v21.n2.a2

Authors: Scott A. Taylor, Maggy Tomova

Institutions: Colby College, University of Iowa

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Colby College

OpenAlex ID: W1987268797