Topology Learning Seminar: The Adams Spectral Sequence

Speaker: William Gollinger

Topology Learning Seminar: The Adams Spectral Sequence

The Adams Spectral Sequence was introduced by Frank Adams in his paper "On The Structure and Application of the Streenrod Algebra" (1958) with applications to the stable homotopy groups of spheres and the Hopf-Invariant One problem. In the context of the stable homotopy category it was soon upgraded to the general problem of computing the coefficients of extraordinary cohomology theories.  In this series of lectures we will outline a construction of the Adams Spectral Sequence following Ravenel's "Green Book", and give applications including computations of some stable homotopy groups of spheres as well as certain Madsen-Tillmann bordism groups which have recently been of interest in the theory of TQFTs. 

The seminar assumes some basic knowledge of algebraic topology (in particular homotopy theory and ordinary homology theory) but is aimed to be expository, introducing the audience to important topological concepts such as stable homotopy theory and cohomology operations. The topics presented will be roughly in the following order: examples of the Leray-Serre spectral sequence; the Stable Homotopy Category; construction of the Adams Spectral Sequence; the Steenrod Algebra and its dual; computations.

MC 5417