Subject: Question regarding equivariant K-theory.
From: Nitu Kitchloo
Date: Mon, 12 Feb 2007 22:49:54 -0800 (PST)
Here is a somewhat simple question about Equivariant K-theory:
Suppose I have a representation of a compact Lie gp G on a general Hilbert
space H (which contains all its subrepresentations infinitely often but
fails to contain all representations), what can I say about the
equivariant
K-theory spectrum K(H) modelled on the Fred.operators on H?
There seems to be a map from K(H) to the standard equivariant K-theory
spectrum. Does that split?
I am mostly interested in the homotopy of S0 \smash_G K(H). Any
information would be welcome.
Nitu.