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:

  1. Brickell, F. and Clark, R. S., Differentiable Manifolds, Van Nostrand Reinhold Co., London, 1970.
  2. Guillemin, V. and Pollack, A., Differential Topology, Prentice Hall, 1974.
  3. Kosniowski, C., A, First Course in Algebraic Topology, Cambridge Univ. Press, 1980.
  4. Milnor, John W., Topology from the Differentiable Viewpoint, Princeton Landmarks in Mathematics, Princeton Univ. Press, 1997.
  5. Munkres, J. R., Elements of Algebraic Topology, Addison-Wesley, 1984.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 23 Feb 2024