Volume 14, issue 2 (2010)

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
The $h$–principle for broken Lefschetz fibrations

Jonathan Williams

Geometry & Topology 14 (2010) 1015–1061
Abstract

It is known that an arbitrary smooth, oriented 4–manifold admits the structure of what is called a broken Lefschetz fibration. Given a broken Lefschetz fibration, there are certain modifications, realized as homotopies of the fibration map, that enable one to construct infinitely many distinct fibrations of the same manifold. The aim of this paper is to prove that these modifications are sufficient to obtain every broken Lefschetz fibration in a given homotopy class of smooth maps. One notable application is that adding an additional “projection" move generates all broken Lefschetz fibrations, regardless of homotopy class. The paper ends with further applications and open problems.

Keywords
broken, Lefschetz fibration, $4$–manifold, stable map
Mathematical Subject Classification 2000
Primary: 57M50, 57N13
Secondary: 57R70, 57R17
References
Publication
Received: 1 July 2009
Accepted: 23 February 2010
Published: 31 March 2010
Proposed: Ron Fintushel
Seconded: Yasha Eliashberg, Simon Donaldson
Authors
Jonathan Williams
Department of Mathematics
The University of Texas at Austin
Austin, Texas 78712
http://ma.utexas.edu/jwilliam