Crosscap number and knot projections

DOI10.1142/S0129167X18500842zbMath1420.57022arXiv2008.11061OpenAlexW3098862246MaRDI QIDQ4561469

Noboru Ito, Yusuke Takimura

Publication date: 6 December 2018

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.11061

zbMATH Keywords

alternating knottorus knotunknotting numberpretzel knotspliceknot diagramcrosscap numberknot projectionrational knot

Mathematics Subject Classification ID

Related Items (8)

PLUMBING AND COMPUTATION OF CROSSCAP NUMBER ⋮ Crosscap number three alternating knots ⋮ When can a link be obtained from another using crossing exchanges and smoothings? ⋮ AUTOMATIC COMPUTATION OF CROSSCAP NUMBER OF ALTERNATING KNOTS ⋮ Raising crosscap number while lowering unknotting number ⋮ Crosscap number of knots and volume bounds ⋮ A lower bound of crosscap numbers of alternating knots ⋮ Crosscap numbers of alternating knots via unknotting splices

Uses Software

• KnotInfo

Cites Work

• Unnamed Item
• Triple chords and strong (1, 2) homotopy
• A classification of spanning surfaces for alternating links
• Crosscap numbers and the Jones polynomial
• Crosscap numbers of pretzel knots
• Incompressible surfaces in 2-bridge knot complements
• State models and the Jones polynomial
• Crosscaps and knots
• Crosscap numbers of torus knots.
• Crosscap number of a knot
• Crosscap numbers of 2-bridge knots
• Computing the Crosscap Number of a Knot Using Integer Programming and Normal Surfaces
• Knot Enumeration Through Flypes and Twisted Splices
• Constructing crosscap number two surfaces from low-complexity handcuff graphs
• THE HALF-TWISTED SPLICE OPERATION ON REDUCED KNOT PROJECTIONS
• The tabulation of prime knot projections with their mirror images up to eight double points

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