Half-turn linked pairs of isometries of hyperbolic 4-space
From MaRDI portal
Publication:2800397
zbMATH Open1337.51008arXiv1311.6356MaRDI QIDQ2800397
Author name not available (Why is that?)
Publication date: 15 April 2016
Published in: (Search for Journal in Brave)
Abstract: In this paper we develop a complete theory of factorization for isometries of hyperbolic 4-space. Of special interest is the case where a pair of isometries is linked, that is, when a pair of isometries can be expressed each as compositions of two involutions, one of which is common to both isometries. Here we develop a new theory of hyperbolic pencils and twisting planes involving a new geometric construction, their half-turn banks. This enables us to give complete results about each of the pair-types of isometries and their simultaneous factorization by half-turns. That is, we provide geometric conditions for each such pair to be linked by half-turns. The main result gives a necessary and sufficient condition for any given pair of isometries to be linked. We also provide a procedure for constructing a half-turn linked pair of isometries of that do not restrict to lower dimensions, yielding an example that gives a negative answer to a question raised by Ara Basmajian and Karan Puri.
Full work available at URL: https://arxiv.org/abs/1311.6356
No records found.
No records found.
This page was built for publication: Half-turn linked pairs of isometries of hyperbolic 4-space
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2800397)
