Course No
M483
Credit
4
Approval
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
- Michael Spivak, “A comprehensive introduction to differential geometry”, Vol. 1, 3rd edition, 1999.
- Frank Warner, “Foundations of differentiable manifolds and Lie groups”, Springer Verlag, 2nd edition, 1983.
- John Lee, “Introduction to smooth manifolds”, Springer Verlag, 2nd edition, 2013.
- Louis Auslander and Robert E. MacKenzie, “Introduction to differentiable manifolds”, Dover, 2nd edition, 2009.