Torus actions on homotopy complex projective spaces

Abstract

We prove that an effective action of a torus T on a homotopy Open image in new windowPm is linear if m < 4 ċ rk(T) − 1. Examples show that the bound is optimal. Combining this with a theorem of Hattori we conclude that the total Pontrjagin class of such a manifold is given by the usual formula (1 + x2)m + 1.