Details of MA4105 (Autumn 2019)
Level: 4  Type: Theory  Credits: 4.0 
Course Code  Course Name  Instructor(s) 

MA4105  Differential Geometry  Sayan Bagchi 
Syllabus 

Basic Theory: Topological manifolds, examples, differentiable manifolds and maps, immersed and imbedded manifolds, submanifolds, partitions of unity, compact manifolds as closed submanifolds of R^{n}.
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. 
Prerequisite 

Analysis III (MA3101), Topology (MA3201) 
References 

Suggested Texts:

Course Credit Options
Sl. No.  Programme  Semester No  Course 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 