In this lecture we prove several flavours of the Universal Coefficients Theorem for cohomology.

Corollary 29.9 is probably the single most useful part of the lecture; this allows you to compute the singular cohomology from the singular homology. This only works for topological spaces of finite type, but almost all interesting (from the point of view of this course, anyway) topological spaces have this property.

Remark

Next Wednesday, Berit is giving the lecture. She will go over the hard questions from Problem Sheet L and Problem Sheet M. So the next “proper” lecture is not until Friday 16th March.