Introduction to Algebraic Topology 

Lecturer: Wu Jie
Office: S14, #0407, Faculty of Science, Lower Kent Ridge Road. 

Review of metric and topological spaces. Constructions and universal properties, product space, subspace and quotient space, collapsing, smash product and orbit spaces. Locally compact Hausdorff spaces and identification maps, compactopen topology. Paths, pathrelated points, pathcomponents. Pathequivalence of paths, the fundamental group and groupoid, change of basepoint, change of space. Homotopy, simplyconnected and contractible spaces, simpleconnectedness of S^{n} . Homotopy invariance of fundamental group. Covering spaces, properly discontinuous group actions. Lifting theorems. Applications, including Fundamental Theorem of Algebra, BorsukUlam Theorem. Properly discontinuous actions and classification of covering spaces.
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