Algebraic Topology

What it is about

You will learn fundamental algebraic invariants of topological spaces and how to apply them. The focus is on singular homology and cohomology as well as their computational methods and applications (e.g. Poincaré duality for manifolds). In the end you can compute these theories on concrete examples and solve typical problems with them.

What you will be able to do

• Understand singular homology
• Apply relative homology and long exact sequences
• Compute cellular homology
• Use homotopy invariance and excision
• Use tensor products and homology with coefficients
• Compute the homology of products
• Understand cohomology and its ring structure
• Apply Poincaré duality for manifolds

What the module consists of

• VorlesungConveying the theoretical foundations and examples on the board
• ÜbungDiscussion and deepening of the exercise tasks to apply the lecture content

Teaching method

• TafelvortragPresentation of theoretical principles and examples
• Übungsaufgaben/SitzungenDiscussion of tasks for illustration and deepening