Ngô Quốc Anh

January 12, 2009

MA5210: Differentiable Manifolds

Filed under: Linh Tinh — Ngô Quốc Anh @ 16:11

Giới thiệu với các bạn problem sets của MA5210 mà tôi phải học ở học kỳ này.

This module studies differentiable manifolds and the calculus on such manifolds. It covers the following topics: tangent spaces and vector fields in Rn, the Inverse Mapping Theorem, differential manifolds, diffeomorphisms, immersions, submersions, submanifolds, tangent bundles and vector fields, cotangent bundles and tensor fields, tensor and exterior algebras, orientation of manifolds, integration on manifolds, Stokes’ theorem. The course is for mathematics graduate students with interest in topology or geometry.


  1. Tangent Spaces, Vector Fields in \mathbb R^n and the Inverse Mapping Theorem: ma5210_tutorial1
  2. Topological Manifolds, Differentiable Manifolds, Diffeomorphisms, Immersions, Submersions and Submanifolds: ma5210_tutorial2
  3. Fibre Bundles and Vector Bundles: ma5210_tutorial3
  4. Tangent Bundles and Vector Fields: ma5210_tutorial4
  5. Cotangent Bundles and Tensor Fields, Tensor Algebras and Exterior Algebras, Orientation of Manifolds, Integration on Manifolds: ma5210_tutorial5
  6. Stokes’ Theorem, DeRham Cohomology: ma5210_tutorial6

Đề thi:

  • Giữa kỳ:
  • Cuối kỳ:

Giáo trình:

  • Lecture Notes
  • Frank W. Warner, Foundations of Differentiable Manifolds and Lie Groups.
  • J.W. Milnor, Topology from the differentiable viewpoint, The University Press of Virginia, Charlottesville.
  • S. Lang, Introduction to differentiable manifolds, Imprint New York , Interscience Publishers.

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