Alternating links on nonorientable surfaces and Klein-bottly alternating links

TL;DR

This paper extends the theory of alternating links to nonorientable surfaces and explores Klein-bottly alternating links in prism manifolds, broadening understanding of hyperbolic properties beyond orientable cases.

Contribution

It introduces the study of alternating links on nonorientable surfaces and applies this to Klein-bottly alternating links in prism manifolds, generalizing previous results.

Findings

Extended hyperbolic geometry results to nonorientable surfaces

Analyzed Klein-bottly alternating links in prism manifolds

Connected nonorientable surface links to classical alternating link theory

Abstract

It has been known for several decades that classical alternating links in the 3-sphere have nice hyperbolic geometric properties. Recent work generalises such results to give hyperbolic geometry of links with alternating projections onto any surface in very general 3-manifolds. However, the most general results require an orientable projection surface. In this paper, we extend to alternating links on nonorientable projection surfaces. As an application, we study Klein bottly alternating links in prism manifolds, which are a natural generalisation of Adams' toroidally alternating links in lens spaces.