Details of MA4206 (Spring 2017)

Level: 4 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA4206 Algebraic Topology Somnath Basu

MA4103 : Algebraic Topology

Homotopy Theory: Homotopy and homotopy equivalence; retraction, deformation retract, contractible spaces; fundamental groups; covering spaces, path lifting and homotopy lifting; fundamental group of S1; Borsuk-Ulam theorem, Van-Kampen theorem; fundamental group of Sn; Brouwers no-retraction and fixed point theorem in dimension two.

Homology Theory: Barycentric subdivision; finite simplicial complexes and their geometric realizations; simplicial approximation theorem; triangulable spaces, triangulation of standard manifolds; simplicial chain complex, simplicial homology; computation of simplicial homology groups of Sn, RPn and Klein bottle.

Suggested Texts/Reference Books:

1. Massey, W. S., A Basic Course in Algebraic Topology, Springer-Verlag, 1991.

2. Munkres, J. R., Elements of Algebraic Topology, Addison-Wesley, 1984.

3. Spanier, E. H., Algebraic Topology, Springer-Verlag, 1966.

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 Not Allowed