On positive scalar curvature bordism

Using standard results from higher (secondary) index theory, we prove that the positive scalar curvature bordism groups Pos^spin_{4n}(G × Z) are infinite for any n ≥ 1 and G a group with non-trivial torsion. We construct representatives of each of these classes which are connected and with fundamental group G × Z. We get the same result for Pos^spin_{4n+2} (G × Z) if G is finite and contains an element which is not conjugate to its inverse. This generalizes the main result of Kazaras, Ruberman, Saveliev, “On positive scalar curvature cobordism and the conformal Laplacian on end-periodic manifolds” to arbitrary even dimensions and arbitrary groups with torsion.