Volume 18, issue 3 (2018)

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Hyperbolic tangle surgeries and nested links

John Harnois, Hayley Olson and Rolland Trapp

Algebraic & Geometric Topology 18 (2018) 1573–1602

Changes to gluing patterns for fully augmented links are shown to result in generalized fully augmented links. The first changes considered result in 4–tangle surgeries on hyperbolic fully augmented links that produce hyperbolic generalized fully augmented links. These surgeries motivate the definition of nested links, and a characterization of hyperbolic nested links is given. Finally, the geometry of nested links is compared to that of fully augmented links.

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hyperbolic link, fully augmented link
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57M50
Received: 3 February 2017
Revised: 6 September 2017
Accepted: 12 September 2017
Published: 3 April 2018
John Harnois
Department of Mathematics
University of Virginia
Charlottesville, VA
United States
Hayley Olson
Department of Mathematics
University of Nebraska
Lincoln, NE
United States
Rolland Trapp
Department of Mathematics
California State University
San Bernardino, CA
United States