Abstract
We develop a theory of link projections to trivalent spines of 3-manifolds. We prove a Reidemeister Theorem providing a set of combinatorial moves sufficient to relate the projections of isotopic links. We also show that any link admits a crossingless projection to any special spine and we refine our theorem to provide a set of combinatorial moves sufficient to relate crossingless diagrams. Finally, we discuss the connection to Turaev’s shadow world, interpreting our result as a statement about shadow equivalence of a class of 4-manifolds.
Original language | English |
---|---|
Pages (from-to) | 1190-1209 |
Number of pages | 20 |
Journal | Discrete and Computational Geometry |
Volume | 71 |
Issue number | 4 |
DOIs | |
Publication status | Published - Jun 2024 |