Locatization techniques in computation of equivariant J-groups and equivariant cross sections of stiefel manifolds
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Let G be a finite group and X be a finite G-connected G-CW complex. The main purpose of this dissertation is to find means for computing the equivariant J-groups, JOG(X), and then to obtain solutions for the equivariant cross section problem of Stiefel manifolds. We give an alternative method for computing JOG(X). We do our computations for the cases: X is a free G-space, X is a trivial G-space, and X is a one point set. We find the orders of elements of JOG(FPk) for various projective spaces, and then we use the results to obtain a partial solution for the equivariant cross section problem of Stiefel manifolds. Without using Atiyah-Segal completion theorem, we prove two methods for computing JO(X). Then we show how to use these methods to find the orders of elements of JO(X), and also to find JO(X). Our illustrative example is CPk, the complex projective space.