Subgroups of Group of homotopy spheres

Abstract

Let θⁿ 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_pS0(q+1) → Π_{p + Q + 1} (S<sup>q+1>)

JONAMP Vol. 11 2007: pp. 47-50</sup>