Volume 2 (1999)

Download this article
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
About this Series
Editorial Board
Ethics Statement
Submission Guidelines
Purchases
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
Author Index
 
MSP Books and Monographs
Other MSP Publications

The E8–manifold, singular fibers and handlebody decompositions

Robion Kirby and Paul Melvin

Geometry & Topology Monographs 2 (1999) 233–258

DOI: 10.2140/gtm.1999.2.233

arXiv: math.GT/9911253

Abstract

The E8–manifold has several natural framed link descriptions, and we give an efficient method (via "grapes") for showing that they are indeed the same 4–manifold. This leads to explicit handle pictures for the perturbation of singular fibers in an elliptic surface to a collection of fishtails. In the same vein, we show how the degeneration of a regular fiber to a singular fiber in an elliptic surface provides rich examples of Gromov's compactness theorem.

Keywords

4–manifolds, handlebodies, elliptic surfaces

Mathematical Subject Classification

Primary: 57N13

Secondary: 14J27, 57R65

References
Publication

Received: 13 October 1999
Published: 19 November 1999

Authors
Robion Kirby
University of California
Berkeley CA 94720
USA
Paul Melvin
Bryn Mawr College
Bryn Mawr PA 19010
USA