# Course

## M483 - Introduction to Manifolds

Course No:
M483
Credit:
4
Prerequisites:
M304
Approval:
UG-Elective
PG-Elective
Syllabus:

Differentiable manifolds and maps: Definition and examples, Inverse and implicit function theorem, Submanifolds, immersions and submersions.The tangent and cotangent bundle: Vector bundles, (co)tangent bundle as a vector bundle, Vector fields, flows, Lie derivative.Differential forms and Integration: Exterior differential, closed and exact forms, Poincare' lemma, Integration on manifolds, Stokes theorem, De Rham cohomology.

Reference Books:
1. Michael Spivak, “A comprehensive introduction to differential geometry”, Vol. 1, 3rd edition, 1999.
2. Frank Warner, “Foundations of differentiable manifolds and Lie groups”, Springer Verlag, 2nd edition, 1983.
3. John Lee, “Introduction to smooth manifolds”, Springer Verlag, 2nd edition, 2013.
4. Louis Auslander and Robert E. MacKenzie, “Introduction to differentiable manifolds”, Dover, 2nd edition, 2009.