Incompressible surfaces in link complements

2000/11/01 by Ying-Qing Wu, Wu, Ying-Qing · 1 citation
Mathematics · #57M25 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.math/0011006

7 pages, 3 figures. To appear in Proc. AMS

arxiv created 2000/11/01 · openalex publication_date 2000/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize a theorem of Finkelstein and Moriah and show that if a link L has a 2n-plat projection satisfying certain conditions, then its complement contains some closed essential surfaces. In most cases these surfaces remain essential after any totally nontrivial surgery on L.

Citations

• Dehn Surgery on Knots

Cited by

• Rigidity of highly twisted plat diagrams

Related

• End-essential spanning surfaces for links in thickened surfaces
• Closed incompressible surfaces of genus two in 3-bridge knot complements
• Non-parallel essential surfaces in knot complements
• Knots with only two strict essential surfaces
• Standard position for surfaces in link complements in arbitrary 3-manifolds