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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