Robert Riley | Searcharxiv

arXiv2013

A personal account of the discovery of hyperbolic structures on some knot complements

I give my view of the early history of the discovery of hyperbolic structures on knot complements from my early work on representations of knot groups into matrix groups to my meeting with William Thurston in 1976. (This article was written by Robert Riley about ten years before his death in 2000 and never submitted for publication. An explanation of why it is being published now and some information about Riley and this article is given in the article by Brin, Jones and Singerman which accompanies this article in this issue of the [journal | arxiv].)

math.HO↗

arXiv2009

Epimorphisms between 2-bridge link groups

We give a systematic construction of epimorphisms between 2-bridge link groups. Moreover, we show that 2-bridge links having such an epimorphism between their link groups are related by a map between the ambient spaces which only have a certain specific kind of singularity. We show applications of these epimorphisms to the character varieties for 2-bridge links and pi_1-dominating maps among 3-manifolds.

math.GT↗