Plan for this course_亚博娱乐官网_亚博pt手机客户端登录

I plan to lecture about foundations and applications of stable homotopy theory.

As motivation, we may study examples of generalized (co)homology theories, such as bordism [Pontryagin, Thom] and $K$-theory [Bott, Atiyah-Hirzebruch]. Such functors become representable in the stable homotopy category [Boardman, Adams], which is triangulated and closed symmetric monoidal. In the 1990s, this structure was found to arise as the homotopy category of a model category, in several ways, including $S$-modules, symmetric spectra and orthogonal spectra [Elmendorf-Kriz-Mandell-May, Hovey-Shipley-Smith, Lydakis, May-Mandell-Schwede-Shipley, ...]. We will follow a book project by Stefan Schwede, titled " Symmetric Spectra", as an introduction to these results. Thereafter we will turn to the equivariant theory [Adams, Lewis-May-Steinberger,...