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The E8–manifold, singular fibers and
handlebody decompositions
Robion Kirby and Paul Melvin
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Geometry & Topology Monographs 2
(1999) 233–258
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Abstract
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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.
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Keywords
4–manifolds, handlebodies, elliptic
surfaces
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Mathematical Subject Classification
Primary: 57N13
Secondary: 14J27, 57R65
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Publication
Received: 13 October 1999
Published: 19 November 1999
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