Algebraic Topology (C3.1a)
Michaelmas Term 2018. Class T12 & W12.
Course description
This is an advanced undergraduate or beginning graduate course in algebraic topology. Topics will include: simplicial, singular, and cellular homology; axiomatic descriptions of homology; cohomology, and cross and cup products; Universal coefficient and Künneth theorems; and Poincaré, Lefschetz, and Alexander duality.
Prerequisites
A3 Rings and Modules is essential, in particular a solid understanding of groups, rings, fields, modules, homomorphisms of modules, kernels and cokernels, and classification of finitely generated abelian groups.
A5 Topology is essential, in paticular a solid understanding of topological spaces, connectedness, compactness, and classification of compact surfaces.
Some but not all material from B2.1 Representation Theory is essential, specifically students must have a solid understanding of tensor products of abelian groups.
Some but not all material from B3.5 Topology and Groups is essential, specifically students must have a solid understanding of homotopic maps, homotopy equivalence, and the fundamental group.
It is recommended, but not required, that students take C2.2 Homological Algebra concurrently.
Syllabus
The syllabus, available here, contains a page of references and background resources, along with information about the classes and problem sheets.
Problem sheets
Contact information
Christopher Douglas
Office: N2.27
Email: cdouglas at maths
