Adams operations on compact Lie groups

Chi-Kwong Fok(霍志广)  (Xi'an Jiaotong-Liverpool University)

10:00-11:00，April 12，2024    ScienceBuilding A503

Abstract:

Adams operations are important cohomological operations on K-theory. According to a theorem of Bousfield, an application of Adams operations is the extraction of certain information on homotopy groups of Lie groups. On the other hand, Atiyah and Segal generalized the definition of Adams operations to twisted K-theory. It would be interesting to explore explicit computational examples in this setting. In particular, via the Freed-Hopkins-Teleman Theorem, Adams operations on twisted K-theory of compact Lie groups provide a good candidate for defining Adams operations on representations of loop groups which are infinite dimensional. In this talk, we will present results on Adams operations on compact Lie groups in both twisted and untwisted settings.

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