Скачать или смотреть Bo Liu: When index theory meets K-theory

In 1956, Hirzebruch generalised the famous Riemann-Roch theorem to higher dimensions, which motivated Grothendieck to introduce the K-theory. On the other hand, Atiyah and Singer proved the index theorem and found that the "home" of the index should be the topological version of the K-theory introduced by Atiyah and Hirzebruch. In 1990s, the development of the arithmetic version of the Riemann-Roch theorem related arithmetic K-theory in Arakelov geometry to analytic torsion, an important secondary invariant in index theory. Recently, motivated by physics, differential K-theory has been well studied and related to the eta invariant and eta form in index theory. In this talk we will discuss some connections between index theory and K-theory, in particular some recent progress on differential K-theory and eta forms.