Primary decomposition of the J-groups of complex projective and lens spaces

Abstract

We determine the decomposition of J-groups of complex projective and lens spaces as a direct-sum of cyclic groups. © 2005 Elsevier B.V. All rights reserved

J-Groups of Lens Spaces modulo Odd Prime Powers

“…But, it is responsible for all complications and the reason behind the messy work [1]. This is also the case for the works [8] and [2].…”

“…The group J(L) is clearly a quotient group of J(BZ p r ) because of Theorem 3. Unfortunately things are very complicated in this quotient, [1], [8]. On the other hand, we can find an upper bound for the group J (L) by determining the order of the elements ψ p s (w).…”

“…J-Groups of lens spaces were studied a lot especially by Japanese mathematicians after J. F. Adam's solution of the vector fields on spheres problem by making use of the J-groups of real projective spaces. In [1], I. Dibag described the group structure of J-Groups of lens spaces modulo prime powers. His work involves heavy elementary number theory.…”