Nearly Euclidean Thurston Maps and the Halfspace Theorem

TR Number
Date
2016-11-14
Journal Title
Journal ISSN
Volume Title
Publisher
Virginia Tech
Abstract

A Thurston map whose postcritical set consists of exactly four points and for which the local degree at each of its critical points is 2 is called textit{nearly Euclidean}. These maps were specified to parse Thurston's combinatorial characterization of rational functions. We determine an extension of the half-space theorem which provides an open hyperbolic half-space such that the negative reciprocal of any fixed slope value is excluded from the boundary of the half-space.

Description
Keywords
Nearly Euclidean Thurston maps, half-space theorem
Citation
Collections