KIT - Department of Mathematics - Sheaf Cohomology in Analysis and Topology (Winter Semester 2014/15)

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Institute of Algebra and Geometry

Research Group Number Theory and Algebraic Geometry

Sheaf Cohomology

Sheaf Cohomology

Sheaf Cohomology in Analysis and Topology (Winter Semester 2014/15)

Lecturer: PD Dr. Fabian Januszewski
Classes: Lecture (0113100)
Audience: Mathematics (from 5. semester)

We will study sheaf cohomology and use it to reinterpret classical results from analysis and topology.

The class may be held in English. Please let me know if you prefer English over German.

Schedule
Lecture:	Tuesday 14:00-15:30	K2

Sheaf cohomology is a powerful tool which allows to connect topology, analysis and other fields of mathematics, and yields to beautiful applications. For example the surjectivity of the complex exponential function ${\rm exp}:{\mathbb C}\to{\mathbb C}^\times$ reflects the fact that the space $\mathbb C$ is contractible.

We will elaborate more on this type of questions, and thereby learn what a sheaf is, what sheaf cohomology is, and how to turn this abstract theory into concrete examples, many of which are beautiful classical results.