Suppose we work with Fréchet algebras. Cuntz defined kk-theory for those algebras and hence we have the notions of K-theory and K-homology for those algebras. Now suppose Chern character is isomorphism in K-theory for those algebras (after tensoring with complex numbers). Does that mean that Chern character is also isomorphism in K-homology (after tensoring with complex numbers)?

  • 1
    $\begingroup$ Usually, what you probably refer to, Chern character is an isomorphism (after tensoring with complex numbers) with one side being K-homology (- not K-theory). To answer your question: unlikely. K-homology = Hom(A,C). K-theory = Hom(C,A). Why should they coincide? Chern character is also defined as a functor from the category $kk_0$ to $HP^0$. So your question seems unprecise. $\endgroup$ – hänsel Mar 12 '16 at 17:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.