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Introduction to Cohomology Operations.
Student-Run Geometry/Topology Seminar| Speaker: | Virgil Chan, UC Davis |
| Location: | 2112 MSB |
| Start time: | Tue, May 19 2015, 1:10PM |
The concept of cohomology operations originated from Norman E. Steenrod's work on classifying maps from a (n+1)-dimensional CW-complex to an n-sphere, up to homotopy. Steenrod later defined a cohomology operation in modulo 2 cohomology, the so-called Steenrod squares, which has numerous applications in algebraic topology (e.g., the formulation of Adams' spectral sequence). We will introduce the notion of cohomology operations, see some examples, and classify them in some cases. We will also go over the construction of Steenrod square, and mention some of its applications. This talk is based on the book ``A Course in Homotopy Topology" by Dmitry B. Fuchs and Anatoly T. Fomenko.