Details of MA5208 (Spring 2020)

Level: 5 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
MA5208 Topology and Geometry Somnath Basu

This course requires approval from the respective instructor for enrolment

Algebraic Topology: Poincare Duality, Kunneth product formula, universal coefficient theorem.

Differential Topology: Transversality and Morse-Sard theorem, distributions and integrability, Frobenius theorem.

Euler Class: Orientation, intersection number, Euler characteristic, Lefschetz fixed point theorem, index of vector field, Poincare-Hopf index theorem, Euler form and Euler class, Euler class of oriented manifolds via Poincare duality.

Instructors consent.

Suggested Texts:

1. Hatcher, A.W., Algebraic Topology, Cambridge University Press.
2. Milnor, J.W. and Stasheff, J., Characteristic Classes, HBA
3. Guillemin, V. and Pollack, A., Differential Topology, Prentice-Hall
4. Hirsch. M., Differential Topology, Springer
5. Bott, R. and Tu, L.W., Differential Forms and Algebraic Topology, Springer

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 2 Not Allowed
2 IP 4 Not Allowed
3 IP 6 Not Allowed
4 MR 2 Not Allowed
5 MR 4 Not Allowed
6 MS 10 Elective
7 RS 1 Not Allowed
8 RS 2 Not Allowed