Volume 24, issue 4 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 5, 2167–2711
Issue 4, 1631–2166
Issue 3, 1087–1630
Issue 2, 547–1085
Issue 1, 1–546

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Salem number stretch factors and totally real fields arising from Thurston's construction

Joshua Pankau

Geometry & Topology 24 (2020) 1695–1716
Abstract

In 1974, Thurston proved that, up to isotopy, every automorphism of a closed orientable surface is either periodic, reducible, or pseudo-Anosov. The latter case has led to a rich theory with applications ranging from dynamical systems to low-dimensional topology. Associated with every pseudo-Anosov map is a real number λ > 1, known as the stretch factor. Thurston showed that every stretch factor is an algebraic unit but it is unknown exactly which units can appear as stretch factors. We show that every Salem number has a power that is the stretch factor of a pseudo-Anosov map arising from a construction due to Thurston. We also show that every totally real number field K is of the form K = (λ + λ1), where λ is the stretch factor of a pseudo-Anosov map arising from Thurston’s construction.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/gt

We have not been able to recognize your IP address 3.81.89.248 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
topology, pseudo-Anosov, Salem number, stretch factor, Thurston's construction, mapping class group
Mathematical Subject Classification 2010
Primary: 11R80, 37E30, 57M99
References
Publication
Received: 16 November 2017
Revised: 21 September 2019
Accepted: 12 December 2019
Published: 10 November 2020
Proposed: Étienne Ghys
Seconded: Bruce Kleiner, Jean-Pierre Otal
Authors
Joshua Pankau
Department of Mathematics
The University of Iowa
Iowa City, IA
United States