Tangential representations of cyclic group actions on homotopy complex projective spaces (Q1064589)

The paper discusses smooth actions of cyclic groups on homotopy complex projective spaces X of dimension 2n. For smooth \(S^ 1\) actions on such spaces Petrie conjectured that the Pontryagin classes of X and \({\mathbb{C}}P^ n\) must coincide (under an identification induced by a homotopy equivalence). The authors produce \({\mathbb{Z}}_ m\) actions on infinitely many such spaces with distinct Pontryagin classes. So, a \({\mathbb{Z}}_ m\) version of Petrie's conjecture does not hold. The methods come from equivariant surgery theory and elementary number theory.