Cohomology complex projective space with degree one codimension-two fixed submanifolds

Karl Heinz Dovermann and Robert D. Little

Vol. 173 (1996), No. 2, 387–401

DOI: 10.2140/pjm.1996.173.387

Abstract

If M²ⁿ is a cohomology ℂPⁿ and p is a prime, let D_p(M²ⁿ) be the set of positive integers d such that d ∈ D_p(M²ⁿ) if there exists a diffeomorphism of M²ⁿ of order p fixing an orientable, codimension-2 submanifold of degree d. If p = 2 or n is odd, then 1 ∈ D_p(M²ⁿ) implies that D_p(M²ⁿ) = {1}. The case p odd and n even is also investigated. If M^4m is a homotopy ℂP^2m and m≢0,4, or 7 (mod 8), then 1 ∈ D₃(M^4m) implies that D₃(M^4m) = {1}.

Mathematical Subject Classification 2000

Primary: 57S17

Secondary: 57R91, 57S25

Milestones

Received: 23 August 1993

Revised: 21 November 1994

Published: 1 April 1996