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Topological K-theory and vector fields on spheres SemesterWiSe 2024 / 25 Lecturer Christoph Winges Type of course (Veranstaltungsart) Seminar German title Topologische K-Theorie und Vektorfelder auf Sphären Contents We will discuss topological K-theory, which is an invariant of topological spaces built in terms of vector bundles over a given space. It turns out that the resulting (contravariant) functor is homotopy invariant and satisfies an appropriate version of the excision theorem, and therefore gives rise to a „generalised cohomology theory“. One of its key additional features is Bott periodicity. After introducing topological K-theory, we will discuss some its classical applications: one can determine the precise number of linearly independent vector fields over spheres, and one can also show that there are no other real division algebras than the reals, the complex numbers, the quaternions and the octonions. Literature Hatcher. Vector Bundles and K-theory; Knapp. Vektorbündel Recommended previous knowledge Analysis, Linear Algebra; some basic notions from topology (eg homotopy) Time/Date tba Location tba Course homepage https://homepages.uni-regensburg.de/~wic42659/ (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BSem, MSem ECTS 4,5 ECTS |