Semifree S3-actions and elliptic genera

There exist a number of results, which relate the characteristic numbers of a compact oriented manifold to the existence of a smooth nontrivial action of the circle group. The present paper deals with the relation of characteristic numbers of a manifold and the existence of a smooth semifree S3-action. One result is the following: If a connected compact oriented manifold admits a nontrivial smooth semifree S3-action, then its Â-genus vanishes.