MA 331: Topology and Geometry
Credits: 3:0
Prerequisite courses: MA 231
Manifolds: Differentiable manifolds, differentiable maps and tangent spaces, regular values and Sard’s theorem, vector fields, submersions and immersions, Lie groups, the Lie algebra of a Lie group.
Fundamental Groups: Homotopy of maps, multiplication of paths, the fundamental group, induced homomorphisms, the fundamental group of the circle, covering spaces, lifting theorems, the universal covering space, Seifert-Van Kampen theorem, applications.
Suggested books and references:
- Brickell, F. and Clark, R. S., Differentiable Manifolds, Van Nostrand Reinhold Co., London, 1970.
- Guillemin, V. and Pollack, A., Differential Topology, Prentice Hall, 1974.
- Kosniowski, C., A, First Course in Algebraic Topology, Cambridge Univ. Press, 1980.
- Milnor, John W., Topology from the Differentiable Viewpoint, Princeton Landmarks in Mathematics, Princeton Univ. Press, 1997.
- Munkres, J. R., Elements of Algebraic Topology, Addison-Wesley, 1984.