Dihedral group actions on homotopy complex projective three spaces

Mark P. Hughes

Vol. 150 (1991), No. 1, 97–110

DOI: 10.2140/pjm.1991.150.97

Abstract

Let D_2m be the dihedral group of order 2m. Given an odd prime m such that the projective class group of D_2m has 2-rank = 0, we construct smooth D_2m-actions on an infinite number of pairwise non-diffeomorphic (distinguished by Pontryagin class) manifolds each of which is homotopy equivalent to CP³. This is accomplished by applying equivariant surgery theory to normal maps created by an equivariant transversality argument.

Mathematical Subject Classification 2000

Primary: 57S25

Secondary: 57S17

Milestones

Received: 8 May 1989

Revised: 10 September 1990

Published: 1 September 1991