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Abstract
This class will focus on those spaces that have a structure of differentiable manifolds and will use, as primary tools, differential forms on them. As a first example of invariants we will consider the de Rham cohomology, namely, spaces of closed forms modulo exact forms.
Objective
Understanding the basic concepts and applying them to a variety of situations.
Content
Algebraic topology consists of algebraic methods devoted to the problem of distinguishing nonhomeomorphic topological spaces (an example of this is the fundamental group discussed in the class Topology). This class will focus on those spaces that have a structure of differentiable manifolds and will use, as primary tools, differential forms on them. As a first example of invariants we will consider the de Rham cohomology, namely, spaces of closed forms modulo exact forms. This approach is "less elementary" than others, as it requires the notions of differentiable manifold and of differential form and as it uses integration as an essential tool. On the other hand, for those that are already familiar with these concepts, it provides a more intuitive approach. Moreover, several results are of direct importance to applications, e.g., in physics.
Resources
Literature
R. Bott and L. W. Tu, Differential Forms in Algebraic Topology, Springer (GTM, volume 82), 1982.
General Information
- Language
- English
- Levels
- BSC , MSC
Examination
- Type
- graded semester performance
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Differential Forms in Algebraic Topology (University of Zurich) | No time listed | 4 h weekly |
| exercise | Differential Forms in Algebraic Topology (University of Zurich) | No time listed | 2 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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