• The second semester is devoted to finishing a few topics from algebraic topology and beginning the study of manifolds. We will give a few more applications of singular homology, define singular cohomology and return to the Van Kampen-Seifert theorem. Then we will turn to manifolds. The assigned text is A Course in Differential Geometry, Thierry Aubin, Graqduate Studies in Mathematics, American Math Society, ISBN 0-8218-2709-X. But we will not work out of a single text. Other relevant books are given below. I had the bookstore order copies of Morita's book as well.

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