Normalizing Topologically Minimal Surfaces I: Global to Local Index

2012/10/16 by David Bachman, Bachman, David · 2 citations
Computer Science · Mathematics · #49Q05 #57M99 #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1210.4573

openalex publication_date 2012/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that in any triangulated 3-manifold, every index n topologically minimal surface can be transformed to a surface which has local indices (as computed in each tetrahedron) that sum to at most n. This generalizes classical theorems of Kneser and Haken, and more recent theorems of Rubinstein and Stocking, and is the first step in a program to show that every topologically minimal surface has a normal form with respect to any triangulation.

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• On the disk complexes of weakly reducible, unstabilized Heegaard splittings of genus three I - the Structure Theorem
• Normalizing Topologically Minimal Surfaces II: Disks

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