What question did this study set out to answer?

The central aim is to extend the Reidemeister theorem to include diagrams of links and bands on 3-manifolds.

February 25, 2026Open Access

Diagrams of Links and Bands on 3-Manifold Spines and Flow-Spines

Puntos clave

The central aim is to extend the Reidemeister theorem to include diagrams of links and bands on 3-manifolds.
Replaced 3-space with any 3-manifold M.
Defined new decorations for diagrams.
Described combinatorial moves relating diagrams of links and bands.
Considered diagrams on almost special spines and flow-spines.
Partially reproves and extends prior results by several researchers.
Introduces new definitions applicable to 3-manifolds.
Demonstrates the relationship of diagrams under isotopy.

Resumen

Abstract The Reidemeister theorem states that any link in 3-space can be encoded by a diagram (a suitably decorated projection) on a plane, and provides a finite set of combinatorial moves relating two diagrams of the same link up to isotopy. In this note we replace 3-space by any 3-manifold M and we extend the Reidemeister theorem (definition of the decoration and description of the combinatorial moves) in four situations, taking diagrams either of links or of bands (collections of cylinders and Möbius strips), either on an almost special spine or on a flow-spine of M . This partially reproves and extends a result of Brand, Burton, Dancso, He, Jackson and Licata.

Me gusta

Guardar

Ver artículo completo