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A reduced set of moves on one-vertex ribbon graphs coming from links


Authors: Susan Abernathy, Cody Armond, Moshe Cohen, Oliver T. Dasbach, Hannah Manuel, Chris Penn, Heather M. Russell and Neal W. Stoltzfus
Journal: Proc. Amer. Math. Soc. 142 (2014), 737-752
MSC (2010): Primary 05C10, 57M15, 57M25
DOI: https://doi.org/10.1090/S0002-9939-2013-11807-1
Published electronically: November 18, 2013
MathSciNet review: 3148509
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Abstract | References | Similar Articles | Additional Information

Abstract: Every link in $ \mathbb{R}^3$ can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.


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Additional Information

Susan Abernathy
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: sabern1@tigers.lsu.edu

Cody Armond
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Address at time of publication: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
Email: cody-armond@uiowa.edu

Moshe Cohen
Affiliation: Department of Mathematics, Bar-Ilan University, Ramat Gan 52900, Israel
Email: cohenm10@macs.biu.ac.il

Oliver T. Dasbach
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: kasten@math.lsu.edu

Hannah Manuel
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Address at time of publication: Department of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: hmanuel3@math.gatech.edu

Chris Penn
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: coffee@math.lsu.edu

Heather M. Russell
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532
Address at time of publication: Department of Mathematics and Computer Science, Washington College, Chestertown, Maryland 21620
Email: hrussell2@washcoll.edu

Neal W. Stoltzfus
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: stoltz@math.lsu.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11807-1
Received by editor(s): December 21, 2011
Received by editor(s) in revised form: April 2, 2012
Published electronically: November 18, 2013
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.