CONCORDANCES OF METRICS OF POSITIVE SCALAR CURVATURE

Spaces of metrics of positive scalar curvature are studied modulo a concordance relation. It is shown that the set of concordance classes of metrics with positive scalar curvature on a dosed manifold of dimension greater-than-or-equal-to 6 depends only on the dimension, the first Stiefel-Whitney class of the manifold, and the cokernel of a homomorphism pi2(M(n)) --> KO(S2). In addition, for every nonneptive integer i the ith concordance group of metrics of positive scalar curvature is defined and it is shown that for a spin manifold the group is nontrivial when n + i = 4k + 3, 8k, 8k + 1, k greater-than-or-equal-to 1.