The E_8-manifold, singular fibers and handlebody decompositions

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.

arXiv comment26 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper13.abs.html

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