Index theory on the Miščenko bundle
Index theory on the Miščenko bundle
We consider the assembly map for principal bundles with fiber a countable discrete group. We obtain an index-theoretic interpretation of this homomorphism by providing a tensor-product presentation for the module of sections associated to the Mi\v{s}\v{c}enko line bundle. In addition, we give a proof of Atiyah's $L^2$-index theorem in the …