Fachbereich Mathematik 
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Higher Structures in Differential Geometry


Content

The lecture will focus mainly on generalisations of finite-dimensional manifolds and their treatment as objects of (pre)sheaves. This will roughly divided into two major parts: The treatment of infinite-dimensional objects, such as manifolds of mappings, and the treatment of categorified objects (objects with internal symmetries), such as Lie groupoids. In both cases the perspective from sheaf theory provides important insights and results, for instance in understanding the "correct" notion of morphism between Lie groupoids, which leads to the description of Lie groupoids as smooth stacks.
Both structures (infinite-dimensional and categorified ones) are important in various parts of modern mathematics, for instance in algebraic geometry and in mathematical physics. I will point out these connections throughout the lecture and can provide literature for further reading on demand.

Lecture Notes

Here is a very preliminary version of the lecture notes that I will provide. Beware: This is a non-proofread working copy of my own notes, so take them with a grain of salt. In particular, I am grateful for any kind of feedback on them.

Exercises

The exercise sheets will be posted above roughly one week before they are discussed (there will be no exercise class in the first week), and will be discussed in the class on Wednesday. The students are supposed to work on the exercises before the class. This means that each student is expected to have worked on at least one exercise and should be able to present a solution or to nail down the problems that she or he has with solving it.

Note that I will not provide solution sheets this semester.

Sheets



 
  Seitenanfang  Impress 2014-06-06, Christoph Wockel