Generalized augmented alternating links and hyperbolic volume

TL;DR

This paper extends the class of augmented alternating links to include n-punctured disks, proving their hyperbolicity and computing volumes for generalized belted sums, thus broadening understanding of hyperbolic link structures.

Contribution

It introduces generalized augmented alternating links with n-punctured disks and establishes their hyperbolicity, expanding the scope of known hyperbolic link classes.

Findings

Generalized augmented alternating links are hyperbolic.

Volumes of generalized belted sums of links are computed.

Extension of hyperbolic volume calculations to new link classes.

Abstract

Augmented alternating links are links obtained by adding trivial components that bound twice-punctured disks to non-split 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.