5
$\begingroup$

This may be a silly question but I don't know the answer.

I know the construction of (equivariant) K-spectrum $KU_G$ and the periodicity of (equivariant) K-theory. But I don't know its structure maps and how they are constructed.

Can anybody show me the answer or some reference on this? Thanks very much.

$\endgroup$
5
$\begingroup$

That is a very reasonable question. By a $G$-spectrum $KU_G$, $G$ a compact Lie group, one should mean a genuine $G$_spectrum, so suitably indexed on representations of $G$. One gets the structure maps by use of equivariant Bott periodicity. A good sketch of how this goes, without full details, is given on pages 146-148 of Equivariant Homotopy and Cohomology Theory (available here: http://www.math.uchicago.edu/~may/BOOKS/alaska.pdf). The relevant chapter was written by John Greenlees.

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.