Surgery of Poincaré complexes

In the paper one studies the problem of extending the method of Morse surgery for the study of smooth manifolds to the case of the category of Poincaré complexes. In the latter case we compute an obstruction to the surgery of a Poincaré complex up to homotopy equivalence which, as in the classical case, is in the Wall group. In contrast to the cases of smooth or combinatorial manifolds we are able to handle only complexes with vanishing boundary.
Bibliography: 3 titles.