Details of MA4105 (Autumn 2019)

Level: 4 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
MA4105 Differential Geometry Sayan Bagchi

Basic Theory: Topological manifolds, examples, differentiable manifolds and maps, immersed and imbedded manifolds, submanifolds, partitions of unity, compact manifolds as closed submanifolds of Rn.

Tangent Space and Vector Fields: Definition of tangent vector as equivalence class of curves and derivations, tangent spaces and their mappings, tangent bundle, vector fields, integral curves, complete vector fields, Lie derivative and connection with Lie bracket of vector fields.

Differential Forms and Integration: Wedge product, Exterior differentiation: definition, axiomatic treatment and coordinate invariance, closed and exact forms, review of classical line and surface integrals, orientation, Stokes theorem.

de Rham Cohomology: Definition, elementary computation for compact orientable surfaces, computation of highest cohomology.

Analysis III (MA3101), Topology (MA3201)


Suggested Texts:

  1. Guillemin, V. and Pollack, A., Differential Topology, AMS Chelsea.

  2. Hirsch, M.W., Differential Topology, Springer.

  3. Kumaresan, S., A Course in Differential Geometry and Lie Groups, Hindustan Book Agency.

  4. Lee, J.M., Introduction to Smooth Manifolds, Springer-Verlag.

  5. Milnor, J,W., Topology from the Differentiable Viewpoint, Princeton University Press.

  6. Mukherjee, A., Topics in Differential Topology, Hindustan Book Agency.

  7. Spivak, M., A comprehensive Introduction to Differential Geometry, Vol. I, 3rd Edition, Publish or Perish.

  8. Tu, L.W., An Introduction to Manifolds, Universitext, Springer-Verlag.

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Not Allowed
2 IP 3 Core
3 IP 5 Not Allowed
4 MR 1 Not Allowed
5 MR 3 Not Allowed
6 MS 7 Elective
7 RS 1 Not Allowed
8 RS 2 Not Allowed