Seminar on Stable Homotopy Theory Ii (ws17/18, Wednesday 16-18, Sfb Seminar-room)
نویسندگان
چکیده
Talk 1 (18.10.2017 – Gesina Schwalbe): Overview of some classical results. Recall the classical theorems of Freudenthal and Hurewicz and some elementary calculations of homotopy groups of spheres. Recall the definition of the stable homotopy groups of spheres and explain the ring structure. Show that the Hopf maps are stably essential, i.e. not stably null-homotopic, using Steenrod operations. Use the Adem relations to show that some products of Hopf maps are also stably essential – explain the idea carefully in one example and quickly discuss a second example. Main references: [4, esp. 4.L], [11, Chapter 1], [10].
منابع مشابه
Seminar on Stable Homotopy Theory (ss17,
Talk 1 (26.04.2017): Introduction to spectra. The purpose of this talk is to introduce the category of spectra. We will follow the classical approach using CW spectra. Introduce the basic definitions and give many examples. This includes: (CW-)spectra, Ω-spectra, maps between spectra, homotopies, homotopy groups of spectra, and (weak) homotopy equivalences. Main references: [1, III.2], [9, Ch. 8].
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