Generalized augmented alternating links and hyperbolic volumes

Adams, Colin

doi:10.2140/agt.2017.17.3375

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Generalized augmented alternating links and hyperbolic volumes

Colin Adams

Algebraic & Geometric Topology 17 (2017) 3375–3397

DOI: 10.2140/agt.2017.17.3375

Abstract

Augmented alternating links are links obtained by adding trivial components that bound twice-punctured disks to nonsplit reduced non- $2$ –braid prime alternating projections. These links are known to be hyperbolic. Here, we extend to show that generalized augmented alternating links, which allow for new trivial components that bound $n$ –punctured disks, are also hyperbolic. As an application we consider generalized belted sums of links and compute their volumes.

Keywords

hyperbolic $3$–manifold, alternating link, augmented alternating link, hyperbolic volume

Mathematical Subject Classification 2010

Primary: 57M50

Secondary: 57M25

References

Publication

Received: 20 October 2015

Revised: 2 March 2017

Accepted: 19 April 2017

Published: 4 October 2017

Authors

Colin Adams
Mathematics and Statistics Department Williams College Williamstown, MA United States
https://sites.williams.edu/cadams/

Volume 17, issue 6 (2017)