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MATH 753: Algebraic
Topology and Differential Forms (Fall 2004)
Instructor:
Peter Kahn
Meeting
Time & Room
This course develops many of the important concepts, techniques
and results of algebraic topology from the viewpoint of differential forms,
using material in the classical book of Bott and Tu. Topics will include
de Rham's Theorem, Mayer-Vietoris theorems, Poincaré duality, some
spectral-sequence theory, and some homotopy theory. If time permits, the
course may include some of Warner's treatment of Hodge theory and/or a
development of the theory of characteristic classes.
Prerequisites: Advanced calculus, linear algebra, and one semester
of algebraic topology. It would be desirable to have some familiarity
with differentiable manifolds and the basic objects used in connection
with manifolds: tangent vectors, vector fields, differentiable forms,
etc.
Last modified:
March 31, 2004
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