CONSTRUCTION OF SPECTRAL TRIPLES STARTING FROM FREDHOLM MODULES

Let (A, H, F) be a p-summable Fredholm module where the algebra A = C Gamma is generated by a discrete group of unitaries in L(H), which is of polynomial growth r. Then we construct a spectral triple (A, H, D) with F = sign D which is q-summable for each q > p + r + 1. In case (A , H, F) is (p, infinity)-summable we obtain (q, infinity) summability of (A, H, D) for each q > p + r + 1. (C) Academie des Sciences/Elsevie r, Paris.