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MATH 652:
Introduction to Differentiable Manifolds (Fall 2006)
Instructor:
James West
Meeting
Time & Room
We shall develop (many of) the basic theorems and apparatus used in
their study. This will include inverse and implicit function theorems
in Euclidean spaces, definition and examples of differrentiable manifolds,
tangent vectors and bundles, functorial passage from vector space constructions
to bundle constructions, vector fields, ordinary differential equations
on manifolds, Lie bracket, Lie derivative and Frobenius' Theorem, Lie
groups and their Lie algebras,
Sard's Theorem, Embedding in Euclidean spaces, tensor algebra, tensor fields,
exterior derivative, integration of differential forms, Stokes' Theorem, De Rham
cohomology groups and applications.
We shall use both Boothby's An Introduction to Differentiable Manifolds
and Differential Geometry, and Conlon's Differentiable Manifolds.
Last modified:
April 25, 2006
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