검색
Article Search

JMB Journal of Microbiolog and Biotechnology

OPEN ACCESS eISSN 0454-8124
pISSN 1225-6951
QR Code

Kyungpook Mathematical Journal 2015; 55(2): 485-506

Published online June 23, 2015

Copyright © Kyungpook Mathematical Journal.

The Forbidden Number of a Knot

Alissa S. Crans1,  Blake Mellor1 and Sandy Ganzell2

1Department of Mathematics, Loyola Marymount University, 1 LMU Drive, Los Angeles, California 90045, USA
2Department of Mathematics and Computer Science, St.~Mary's College of Maryland, St.~Mary's City, MD 20686, USA

Abstract

Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and  the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the {it forbidden number}. We relate the forbidden number to several known invariants, and calculate bounds for some classes of
virtual knots.

Keywords: virtual knot, forbidden move, odd writhe