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Manifold aspects of the Novikov Conjecture

Many surveys have been written on the Novikov Conjecture. The goal here is to give an old-fashioned point of view, and emphasize connections with characteristic classes and the topology of manifolds. For more on the topology of manifolds and the Novikov Conjecture see [58], [47], [17]. This article ignores completely connections with C§-algebras (see the articles of Mishchenko, Kasparov, and Rosenberg in [15]), applications of the Novikov conjecture (see [58],[9]), and most sadly, the beautiful work and mathematical ideas uncovered in proving the Novikov Conjecture in special cases (see [14]). The level of exposition in this survey starts at the level of a reader of Milnor-StasheAE’s book Characteristic Classes, but by the end demands more topological prerequisites. Here is a table of contents: