The E_8-manifold, singular fibers and handlebody decompositions

Details The E_8-manifold, singular fibers and handlebody decompositions The E_8-manifold, singular fibers and handlebody decompositions

1999-11-19

arxiv.org/abs/math/9911253v1

Geom. Topol. Monogr. 2 (1999), 233-258

Mathematics

Geometric Topology

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

Scientific paper

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.

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