On positive scalar curvature cobordisms and the conformal Laplacian on end-periodic manifolds

We show that the periodic ?-invariant of Mrowka, Ruberman and Saveliev provides an obstruction to the existence of cobordisms with positive scalar curvature metrics between manifolds of dimensions 4 and 6. Our proof combines the end-periodic index theorem with a relative version of the Schoen-Yau minimal surface technique. As a result, we show that the bordism groups O- n+1(spin,+) (S-1 x BG) are infinite for any non-trivial group G which is the fundamental group of a spin spherical space form of dimension n = 3 or 5.