Canal-U

Sylvain Maillot - An introduction to open 3-manifolds (Part 4)

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

In these lectures, we will focus on two aspects of the subject:

(1) constructing interesting examples, and

(2) finding sufficientconditions that rule out exotic examples, in particular inconnection with Riemannian geometry.