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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.
- Tangent Spaces, Vector Fields in and the Inverse Mapping Theorem: ma5210_tutorial1
- Topological Manifolds, Differentiable Manifolds, Diffeomorphisms, Immersions, Submersions and Submanifolds: ma5210_tutorial2
- Fibre Bundles and Vector Bundles: ma5210_tutorial3
- Tangent Bundles and Vector Fields: ma5210_tutorial4
- Cotangent Bundles and Tensor Fields, Tensor Algebras and Exterior Algebras, Orientation of Manifolds, Integration on Manifolds: ma5210_tutorial5
- Stokes’ Theorem, DeRham Cohomology: ma5210_tutorial6
- Giữa kỳ:
- Cuối kỳ:
- 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.