Subgroups of Group of homotopy spheres

Abstract

Let θ n denote the group of h-cobordism classes of homotopy n-sphere under the connected sum operation. H(p, q) is the subgroup of θ p consisting of those homotopy p-spheres ∑ p such that ∑ p x S w is diffeomorphic to S p x S q . Also bP p+1 is the subgroup of homotopy p-sphere which bounds parallelizable manifolds. In this paper, we will prove that H(p,q) bP p+1 is isomorphic to the Cokernel of Hopf-Whitehead homorphism J : Π p S0(q+1) → Π p + Q + 1 (S q+1>) JONAMP Vol. 11 2007: pp. 47-50