#### 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
##### 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.