Hyperbolic tangle surgeries and nested links

Harnois, John; Olson, Hayley; Trapp, Rolland

doi:10.2140/agt.2018.18.1573

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Hyperbolic tangle surgeries and nested links

John Harnois, Hayley Olson and Rolland Trapp

Algebraic & Geometric Topology 18 (2018) 1573–1602

DOI: 10.2140/agt.2018.18.1573

Abstract

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.

Keywords

hyperbolic link, fully augmented link

Mathematical Subject Classification 2010

Primary: 57M25

Secondary: 57M50

References

Publication

Received: 3 February 2017

Revised: 6 September 2017

Accepted: 12 September 2017

Published: 3 April 2018

Authors

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

Volume 18, issue 3 (2018)