Parity on based matrices
arXiv:2110.04915
Abstract
A parity is a labeling of the crossings of knot diagrams which is compatible with Reidemeister moves. We define the notion of parity for based matrices -- algebraic objects introduced by V. Turaev in his research of virtual strings. We present the reduced stable parity on based matrix which gives a new example of a parity of virtual knots.
The paper is an updated version of the talk on the 5th China-Russia Workshop on Knot Theory and Related Topics, Dalian, 2018