This paper has been replace by a corrected version, so the dvi file here has been removed.
Why do the analytic proofs of the Novikov conjecture require the introduction of C*-algebras?
Why do the analytic proofs of the Novikov conjecture all use $K$-theory instead of $L$-theory? Aren't they computing the wrong thing? (In this connection we discuss in detail how the various (algebraic) $L$-theory spectra of a real or complex C*-algebra are related to its TOPOLOGICAL $K$-theory spectrum.)
How can one show that the index map $\mu$ or $\beta$ studied by operator theorists matches up with the assembly map in surgery theory?
Where does ``bounded surgery theory'' appear in the analytic proofs? Can one find a correspondence between the sorts of arguments used by analysts and the controlled surgery arguments used by topologists?