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Subgroups of Group of homotopy spheres


SO Ajala

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 θp consisting of those homotopy p-spheres ∑ p such that ∑ p x Sw is diffeomorphic to Sp x Sq. Also bPp+1 is the subgroup of homotopy p-sphere which bounds parallelizable manifolds. In this paper, we will prove that H(p,q)bPp+1 is isomorphic to the Cokernel of Hopf-Whitehead homorphism J: ΠpS0(q+1) → Πp + Q + 1 (Sq+1>)

JONAMP Vol. 11 2007: pp. 47-50

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eISSN: 1116-4336