Parity biquandle

• Autorzy: Aaron Kaestner , Louis H. Kauffman
• Języki publikacji: EN

Abstrakty

EN

We use crossing parity to construct a generalization of biquandles for virtual knots which we call parity biquandles. These structures include all biquandles as a standard example referred to as the even parity biquandle. We find all parity biquandles arising from the Alexander biquandle and quaternionic biquandles. For a particular construction named the z-parity Alexander biquandle we show that the associated polynomial yields a lower bound on the number of odd crossings as well as the total number of real crossings and virtual crossings for the virtual knot. Moreover we extend this construction to links to obtain a lower bound on the number of crossings between components of a virtual link.

Kategorie tematyczne

• 57M25: Knots and links in S 3

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2014
• Tom: 100
• Numer: 1
• Strony: 131-151

Daty

wydano

2014

Twórcy

autor

Aaron Kaestner

• Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7045, USA

autor

Louis H. Kauffman

• Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7045, USA

Identyfikatory

DOI

10.4064/bc100-0-7