Generalized augmented alternating links and hyperbolic volumes

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.