Instructor: Uli Wagner
Teaching Assistant: Isaac Mabillard
Class: Mon 13:45-15:00, Wed 14:00-15:15 (Mondi 3)
Recitation: Wed 15:15-16:00 (Mondi 3)
In this course, we will discuss higher-dimensional analogues of graph planarity, namely embeddings of finite simplicial complexes (compact polyhedra) into Euclidean space, and applications, e.g., in discrete geometry and combinatorics.
We will discuss some classical topological aspects like different kinds of embeddings (linear (“straight”) embeddings, piecewise linear embeddings and topological embeddings) and classical tools like deleted products, obstructions, the Whitney trick and the Haefliger-Weber theorem.
We will also discuss combinatorical and algorithmic questions, e.g.: Is there an algorithm that decides whether a given complex embeds in a given dimension?
We will try to adapt the course to the students’ background. Some mathematical maturity will certainly required, but we will try to assume as little prior topological background as possible and introduce or recall the necessary concepts and facts (e.g., about homology and cohomology) along the way.
Lectures and recitations, homework, and an exam at the end of the half-term.
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