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Institut Fourier·S. Maillot
1:16:49
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An Introduction to Open 3-Manifolds (Part 1)
The first part of a lecture series exploring the complex structure and behavior of noncompact 3-manifolds, contrasting them with the well-understood compact manifolds under Thurston's geometrization program.
W. Thurston's geometrization program has lead to manyoutstanding results in 3-manifold theory. Thanks to worksof G. Perelman, J. Kahn and V. Markovic, D. Wise, and I. Agol among others, compact 3-manifolds can now beconsidered to be reasonably well-understood.By contrast, noncompact 3-manifolds remainmuch more mysterious. There is a series of examples,beginning with work of L. Antoine and J. H. C. Whitehead,which show that open 3-manifolds can exhibit wildbehavior at infinity. No comprehensive structure theoryanalogous to geometrization à la Thurston is currently availablefor these objects