The [formula omitted]-genus of [formula omitted]-manifolds with finite second homotopy group

Abstract

We construct simply connected smooth manifolds M of dimension 4 k ⩾ 8 with the following properties: the second homotopy group π 2 ( M ) is finite, M admits a smooth action by the circle S 1 and the A ˆ -genus A ˆ ( M ) is non-zero.