Georgia Institute of Technology College of Sciences

We show that for any connected sum of lens spaces L there exists a connected sum of lens spaces X such that X is rational homology cobordant to L and if Y is rational homology cobordant to X, then there is an injection from H_1(X; Z) to H_1(Y; Z). Moreover, as a connected sum of lens spaces, X is uniquely determined up to orientation preserving diffeomorphism. As an application, we show that the natural map from the Z/pZ homology cobordism group to the rational homology cobordism group has large cokernel, for each prime p. This is joint work with Paolo Aceto and Daniele Celoria.