Arc diagrams on 3-manifold spines
Geometric Topology
2024-05-13 v3
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.
Cite
@article{arxiv.2202.02007,
title = {Arc diagrams on 3-manifold spines},
author = {Jack Brand and Benjamin A. Burton and Zsuzsanna Dancso and Alexander He and Adele Jackson and Joan Licata},
journal= {arXiv preprint arXiv:2202.02007},
year = {2024}
}
Comments
17 pages, 18 figures. v2: Extended references, added some questions and remarks, acknowledgements, and minor clarifications. v3: Minor correction in Lemma 2.3