A+ CATEGORY SCIENTIFIC UNIT

Parity biquandle

Volume 100 / 2014

Aaron Kaestner, Louis H. Kauffman Banach Center Publications 100 (2014), 131-151 MSC: 57M25. DOI: 10.4064/bc100-0-7

Abstract

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.

Authors

  • Aaron KaestnerDepartment of Mathematics, Statistics, and Computer Science
    University of Illinois at Chicago
    Chicago, IL 60607-7045, USA
    e-mail
    e-mail
  • Louis H. KauffmanDepartment of Mathematics, Statistics, and Computer Science
    University of Illinois at Chicago
    Chicago, IL 60607-7045, USA
    e-mail

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