Knot projections with a single multi-crossing

@article{Adams2012KnotPW,
  title={Knot projections with a single multi-crossing},
  author={C. Adams and T. Crawford and B. Demeo and M. Landry and A. Lin and MurphyKate Montee and Seojung Park and S. Venkatesh and Farrah Yhee},
  journal={Journal of Knot Theory and Its Ramifications},
  year={2012},
  volume={24},
  pages={1550011}
}
  • C. Adams, T. Crawford, +6 authors Farrah Yhee
  • Published 2012
  • Mathematics
  • Journal of Knot Theory and Its Ramifications
  • An n-crossing is a singular point in a projection of a link at which n strands cross such that each strand travels straight through the crossing. We introduce the notion of an ubercrossing projection, a knot projection with a single n-crossing. Such a projection is necessarily composed of a collection of loops emanating from the crossing. We prove the surprising fact that all knots have a special type of ubercrossing projection, which we call a petal projection, in which no loops contain any… CONTINUE READING
    25 Citations
    Triple Crossing Number of Knots and Links
    • 30
    • PDF
    Multi-crossing Number for Knots and the Kauffman Bracket Polynomial
    • 7
    • Highly Influenced
    • PDF
    Quadruple crossing number of knots and links
    • 10
    • PDF
    Petal Projections, Knot Colorings and Determinants
    • PDF
    Triple-crossing number and moves on triple-crossing link diagrams
    • 6
    • PDF
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    • PDF

    References

    SHOWING 1-9 OF 9 REFERENCES
    Triple Crossing Number of Knots and Links
    • 30
    • PDF
    Quadruple crossing number of knots and links
    • 10
    • PDF
    THE PROJECTION STICK INDEX OF KNOTS
    • 9
    Embedding knots and links in an open book I: Basic properties
    • 121
    An upper bound of arc index of links
    • 47
    Polygon indices and superbridge indices of torus knots and links
    • 41
    New invariants in the theory of knots
    • 222
    • PDF
    Knots and Links: Preface
    • 87