[Topology.beta] Lecture notes alg top II

[Rot, T.O. (Thomas)]

Dear all,

Renee and I have taught the course algebraic topology 2.

We focused on fiber bundles, and various alg top tools that can help one to understand them. Attached are the notes of the course. We emphasized the geometric/topological side and were example driven.  We assume the reader has seen homology/cohomology but not the cup product. (IN some remarks we assume the reader knows about Eilenbergmaclane spaces and representability of cohomology, but this is not essential)

We treat


  *   Fiber bundles / fiber bundles with structure group  / Principal bundles
  *   Classification of fiber bundles with structure group
  *   Long exact sequence in homotopy groups of a fiber bundle and fibration
  *   The cup product and the kunneth formula
  *   Characteristic classes and cohomology of grassmannians
  *   Poincare duality
  *   Cobordism and a brief introduction to spectra

Questions and remarks are of course welcome. I am sure that there are plenty of typos in the current version.

We will teach the course again in spring 2027.

Best,
Thomas
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