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Topological Manifolds Student: Joe Erickson (erickson@bucks.edu)
September 6, 2014 - Topological manifolds is a subject that appeals to my generalist tendencies, since it straddles point-set topology and algebraic topology, and also employs tools from analysis (especially when moving on to smooth manifolds), algebra, and geometry. Many of the developments here will be recycled in the Algebraic Topology section of this site. The primary reference will be the 2nd edition of John Lee's Introduction to Topological Manifolds. I cannot say when this project will get going, since I start a PhD program at Drexel University in a little over two weeks.
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Document Links
1. Topological Spaces
2. Constructing New Spaces 3. Connectedness & Compactness 4. Cell Complexes 5. Compact Surfaces 6. The Fundamental Group 7. The Circle 8. Free Products & Free Groups 9. The Seifert-Van Kampen Theorem 10. Covering Maps 11. The Classification Theorem |
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