No Access

CUBE NUMBER CAN DETECT CHIRALITY AND LEGENDRIAN TYPE OF KNOTS

BEN MCCARTY

Louisiana State University, 303 Lockett Hall, Baton Rouge, LA 70803, USA

https://doi.org/10.1142/S0218216511009662Cited by:3 (Source: Crossref)

Abstract

For a knot K the cube number is a knot invariant defined to be the smallest n for which there is a cube diagram of size n for K. Examples of knots for which the cube number detects chirality are presented. An example is also presented of two Legendrian knots that, while topologically isotopic, are distinguished as Legendrian knots by cube number.

Keywords:

AMSC: 57M25, 57M27

References

Y. Bae and C. Park, Math. Proc. Cambridge Philos. Soc. 129(3), 491 (2000). Crossref, Web of Science, Google Scholar
S. Baldridge and A. Lowrance, Cube diagrams and a homology theory for knots, preprint (2008) , arXiv:0811.0225v1 . Google Scholar
S. Baldridge and A. Lowrance, Cube knot calculator, http://cubeknots.googlecode.com . Google Scholar
S. Baldridge and B. McCarty, Topology Proc. 36, 213 (2010). Google Scholar
J. C. Cha and C. Livingston, KnotInfo: Table of knot invariants, http://www.indiana.edu/~knotinfo (2009) . Google Scholar
P. Cromwell, Topol. Appl. 64(1), 37 (1995), DOI: 10.1016/0166-8641(94)00087-J. Crossref, Web of Science, Google Scholar
M. Culler and Gridlink, http://www.math.uic.edu/~culler/gridlink/ . Google Scholar
J. B. Etnyre and K. Honda, J. Symplectic Geom. 1(1), 63 (2001). Crossref, Web of Science, Google Scholar
L. Ng, On arc index and maximal Thurston–Bennequin number, preprint (2006) , arXiv:math/0612356v3 . Google Scholar
P. Ozsváth, Z. Szabó and D. Thurston, Legendrian knots, transverse knots and combinatorial Floer homology, preprint (2006) , arXiv:math/0611841v2 . Google Scholar