Title: Homotopy invariance of Novikov-Shubin invariants and $L^2$ Betti numbers
Abstract: We give short proofs of the Gromov-Shubin theorem on the homotopy invariance of the Novikov-Shubin invariants and of the Dodziuk theorem on the homotopy invariance of the $L^2$ Betti numbers of the universal covering of a closed manifold in this paper. We show that the homotopy invariance of these invariants is no more difficult to prove than the homotopy invariance of ordinary homology theory.