The Link Volumes of some prism manifolds

TL;DR

This paper calculates the link volume for an infinite family of prism manifolds, revealing that unlike hyperbolic volume, link volume is not finite-to-one, thus expanding understanding of 3-manifold invariants.

Contribution

It provides explicit calculations of link volumes for prism manifolds and demonstrates a key difference from hyperbolic volume regarding finiteness.

Findings

Link volume is finite for the studied prism manifolds.

Link volume is not finite-to-one, contrasting hyperbolic volume.

Provides explicit formulas for link volumes of certain manifolds.

Abstract

In arxiv:1205.1274 Rieck and Yamashita defined the link volume of 3-manifolds and studied some of its basic properties. Many of these properties are similar to the corresponding properties of the hyperbolic volume. In this paper we calculate the link volume of an infinite family of prism manifolds. As a corollary, we show that (in contrast to the hyperbolic volume) the link volume is not finite-to-one.