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First I'll review some of the definitions from Ken Richardson's earlier talk on the statement and history of the Poincaré Conjecture. The main topic here is 3-manifolds. In general, an n-manifold is a space that can be covered by open unit balls from Rn. On page 2, examples (a) and (d) are 1-manifolds, while the other two are not ((b) fails because of the right endpoint while (c) fails because of the center). |