Details of MA4206 (Spring 2019)

Level: 4 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
MA4206 Algebraic Topology Somnath Basu

Syllabus
Fundamental Group: Path homotopy, definition of fundamental group, covering spaces, path and homotopy lifting, fundamental group of S1, deformation retraction, Brouwer's fixed point theorem, Borsuk-Ulam theorem, van-Kampen's theorem, fundamental group of surfaces, universal covering space, correspondence between covering spaces and subgroups of fundamental group.

Homology Theory: Simplicial complexes and maps, homology groups, computation for surfaces, two definitions of Euler characteristic.

Prerequisite
Topology (MA3201)

References
Suggested Texts:
1. Hatcher, A., Algebraic Topology, Cambridge University Press
2. Massey, W.S., A Basic Course in Algebraic Topology, Springer-Verlag.
3. Munkres, J.R., Elements of Algebraic Topology, Addison-Wesley.
4. Spanier, E.H., Algebraic Topology, Springer-Verlag.

Course Credit Options

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