A calculus for S^3-diagrams of manifolds with boundary
Bojana Femic, Vladimir Grujic, Jovana Obradovic, Zoran Petric
TL;DR
This paper develops a diagrammatic language and calculus for representing and manipulating compact, orientable 3-manifolds with boundary, including proofs of completeness and a finite set of local moves.
Contribution
It introduces a new diagrammatic language and a complete calculus for 3-manifolds with boundary, including integral and rational versions.
Findings
A diagrammatic language for 3-manifolds with boundary
A complete calculus with local moves
Finite set of moves for manifold manipulation
Abstract
We introduce a diagrammatic language for compact, orientable 3-dimensional manifolds with boundary. A diagrammatic calculus (both integral and rational version) appropriate for this language is introduced and its completeness is proved in the paper. Moreover, a calculus consisting of a finite list of local moves is presented.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Computational Geometry and Mesh Generation