Parity biquandle

Aaron Kaestner, and Louis H. Kauffman. "Parity biquandle." Banach Center Publications 100.1 (2014): 131-151. <http://eudml.org/doc/281637>.

@article{AaronKaestner2014,
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.},
author = {Aaron Kaestner, Louis H. Kauffman},
journal = {Banach Center Publications},
keywords = {parity biquandle; quandle; z-parity Alexander polynomial},
language = {eng},
number = {1},
pages = {131-151},
title = {Parity biquandle},
url = {http://eudml.org/doc/281637},
volume = {100},
year = {2014},
}

TY - JOUR
AU - Aaron Kaestner
AU - Louis H. Kauffman
TI - Parity biquandle
JO - Banach Center Publications
PY - 2014
VL - 100
IS - 1
SP - 131
EP - 151
AB - 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.
LA - eng
KW - parity biquandle; quandle; z-parity Alexander polynomial
UR - http://eudml.org/doc/281637
ER -