Gauss diagrams of 3-manifolds

2003/08/06 by Anna Klebanov, Klebanov, Anna
Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M27 #msc:57N10

paper · pdf · doi:10.48550/arxiv.math/0308055

23 pages, 19 figures; to appear in JKTR

arxiv created 2003/08/06 · arxiv updated 2009/12/01

Abstract

We present a simple combinatorial method to encode 3-dimensional manifolds, based on their Heegaard diagrams. The notion of a Gauss diagram of a 3-manifold is introduced. We check the conditions for a Gauss diagram to represent a closed manifold and a manifold with boundary.

Related

• 3-manifolds as viewed from the curve complex
• Grid diagrams and Heegaard Floer invariants
• Triangulated Manifolds with Few Vertices: Geometric 3-Manifolds
• On a computer recognition of 3-manifolds
• A combinatorial description of the U²=0 version of Heegaard Floer\n homology