On the proper homotopy type of locally compact A^2_n-polyhedra
  In this paper we address the classification problem for locally compact (n-1)-connected CW-complexes with dimension less or equal than n+2 up to proper homotopy type. We obtain complete classification theorems in terms of purely algebraic data in those cases where the representation type of the involved algebra is finite. For this we define new quadratic functors in controlled algebra and new homotopy and cohomology invariants in proper homotopy theory. 
Fernando Muro