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MATH 652
Differentiable Manifolds I
(Fall 2003)
Instructor:
Brian Smith
Meeting
Time & Room
This is an introduction to differential geometry at the
level of the beginning graduate student. The prerequisites are advanced
calculus, linear algebra, and point set topology. The topics covered will
include: topological manifolds, differentiable manifolds, immersions and
embeddings, tangent bundles, fibre bundles, vector fields and dynamical
systems, Frobenius' theorem, Lie groups, differential forms, integration
on manifolds, Stokes theorem, connections, Riemannian manifolds, geodesics,
curvature. The last four topics are also covered quite thoroughly in MATH
662 and so they will probably be discussed to a lesser extent than the
other topics. As time permits, we will also cover as much Hodge theory
as possible, and we may also have time to discuss additional topics as
requested by the students.
Last modified:
August 13, 2003
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