Vol. 14, No. 3, 2021

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Reidemeister moves in Gauss diagrams

Sandy Ganzell, Ellen Lehet, Cristina Lopez, Gilbert Magallon and Alyson Thompson

Vol. 14 (2021), No. 3, 431–438
Abstract

Recognizing and performing Reidemeister moves in Gauss diagrams is a useful technique for manipulating virtual knots. For R1 and R2 moves, this process is well understood. We review these cases and then provide a new, elementary algorithm for recognizing R3 moves.

Keywords
Reidemeister moves, Gauss diagram, virtual knot
Mathematical Subject Classification
Primary: 57K10, 57K12
Milestones
Received: 18 July 2020
Revised: 9 December 2020
Accepted: 26 February 2021
Published: 17 July 2021

Communicated by Kenneth S. Berenhaut
Authors
Sandy Ganzell
Department of Mathematics and Computer Science
St. Mary’s College of Maryland
St. Mary’s City, MD
United States
Ellen Lehet
Philosophy Department
University of Notre Dame
Notre Dame, IN
United States
Cristina Lopez
Pomona College
Claremont, CA
United States
Gilbert Magallon
San Diego City College
San Diego, CA
United States
Alyson Thompson
Department of Mathematics and Computer Science
St. Mary’s College of Maryland
St. Mary’s City, MD
United States