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### Geometric and analytic implications of the fundamental group; or, playing the Novikov game

**Colloquium**

Speaker: | Shmuel Weinberger, University of Chicago |

Location: | 1147 MSB |

Start time: | Tue, Oct 3 2006, 4:10PM |

In this talk I will try to explain an important way in which the fundamental group of a manifold controls certain aspects of its geometric topology, differential geometry, and (when relevant) complex geometry. The first example of this idea was due to Novikov who conjectured restrictions on the tangent bundles of nonsimply connected manifolds. By now there are many such examples. This problem is directly connected to both elliptic operators on manifolds and to quadratic form theory and more indirectly connected to algebraic K-theory, rigidity theory, and stratified spaces. My main goals are to explain how to play the Novikov game, and how one can sometimes win.