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Proceedings of the American Mathematical Society Series B

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The Big Dehn Surgery Graph and the link of $S^3$


Authors: Neil R. Hoffman and Genevieve S. Walsh
Journal: Proc. Amer. Math. Soc. Ser. B 2 (2015), 17-34
MSC (2010): Primary 57M25; Secondary 57M50
DOI: https://doi.org/10.1090/bproc/20
Published electronically: November 13, 2015
MathSciNet review: 3422666
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Abstract: In a talk at the Cornell Topology Festival in 2004, W. Thurston discussed a graph which we call “The Big Dehn Surgery Graph”, $\mathcal {B}$. Here we explore this graph, particularly the link of $S^3$, and prove facts about the geometry and topology of $\mathcal {B}$. We also investigate some interesting subgraphs and pose what we believe are important questions about $\mathcal {B}$.


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Additional Information

Neil R. Hoffman
Affiliation: School of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010, Australia
MR Author ID: 813377
Email: nhoffman@ms.unimelb.edu.au

Genevieve S. Walsh
Affiliation: Department of Mathematics, Bromfield-Pearson Hall, Medford, MA, USA
MR Author ID: 720923
Email: genevieve.walsh@tufts.edu

Received by editor(s): March 25, 2015
Received by editor(s) in revised form: June 5, 2015, and July 29, 2015
Published electronically: November 13, 2015
Dedicated: Dedicated to Bill Thurston
Communicated by: Martin Scharlemann
Article copyright: © Copyright 2015 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)