Geometry & Topology Monographs 2 (1999), Proceedings of the Kirbyfest, paper no. 13, pages 233-258.

The E_8-manifold, singular fibers and handlebody decompositions

Robion Kirby, Paul Melvin

Abstract. The E_8-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

AMS subject classification. Primary: 57N13. Secondary: 57R65,14J27.

E-print: arXiv:math.GT/9911253

Submitted: 13 October 1999. Published: 19 November 1999.

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Robion Kirby, Paul Melvin
University of California, Berkeley, CA 94720, USA
Bryn Mawr College, Bryn Mawr, PA 19010, USA
Email: kirby@math.berkeley.edu, pmelvin@brynmawr.edu

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