Lecture course "`Algebraic Topology IV, SoSe 14"'

Contents of the course:

The forth part of the course on algebraic topology gives a systematic study of cohomology theories via the so-called spectra.

The spectra in algebraic topology are a basic tool in homotopy theory. The short description is: spectra are a generalization of topological spaces, where the suspension construction has an inverse: every spectrum is a suspension of some other spectrum (at least upto homotopy equivalence). As a consequence, spectra often have homotopy groups in negative degrees.

It turns out that to every spectrum one can associated a generalized (co)homology theory, and that, on the other hand, every such is represented by a spectrum. Transformations of generalized cohomology theories correpond to maps of spectra.

In the course we will

homology and cohomology, homotopy groups, fibrations. Not required: knowledge of spectral sequences.

Literature (among others):