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An approach to the topological classification of 4-manifolds I

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Matthias Kreck
Univ. Bonn
Tue, 02/04/2013 - 10:30 - 12:00
MPIM Lecture Hall

The starting point is Freedman's disc theorem for 4-manifolds with "good" fundamental group. This has two immediate consequences: The topological s-cobordism theorem and topological surgery in dimension 4. The first reduces the topological classification to the classification up to s-cobordism, the second can be used in constructing topological 4-manifolds. I will introduce into my modified surgery theory which allows a simplified approach to both problems. In particular the topological 4-dimensional Poincare conjecture will follow as well as the characterization of manifolds homeomorphic to $R^4$.

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