Arc Diagrams on 3-Manifold Spines

Jack Brand, Benjamin A. Burton, Zsuzsanna Dancso*, Alexander He, Adele Jackson, Joan Licata

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    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 languageEnglish
    Pages (from-to)1190-1209
    Number of pages20
    JournalDiscrete and Computational Geometry
    Volume71
    Issue number4
    DOIs
    Publication statusPublished - Jun 2024

    Fingerprint

    Dive into the research topics of 'Arc Diagrams on 3-Manifold Spines'. Together they form a unique fingerprint.

    Cite this