Volume 10, issue 4 (2006)

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

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

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
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Universal circles for quasigeodesic flows

Danny Calegari

Geometry & Topology 10 (2006) 2271–2298

arXiv: math.GT/0406040

Abstract

We show that if M is a hyperbolic 3–manifold which admits a quasigeodesic flow, then π1(M) acts faithfully on a universal circle by homeomorphisms, and preserves a pair of invariant laminations of this circle. As a corollary, we show that the Thurston norm can be characterized by quasigeodesic flows, thereby generalizing a theorem of Mosher, and we give the first example of a closed hyperbolic 3–manifold without a quasigeodesic flow, answering a long-standing question of Thurston.

Keywords
quasigeodesic flows, universal circles, laminations, Thurston norm, 3-manifolds
Mathematical Subject Classification 2000
Primary: 57R30
Secondary: 37C10, 37D40, 53C23, 57M50
References
Forward citations
Publication
Received: 15 June 2004
Revised: 10 September 2006
Accepted: 25 October 2006
Published: 29 November 2006
Proposed: David Gabai
Seconded: Benson Farb, Walter Neumann
Authors
Danny Calegari
Department of Mathematics
California Institute of Technology
Pasadena CA, 91125
USA