Thick Spanier groups and the first shape group

Abstract

We develop a new route through which to explore $\ker {\Psi }_X$, the kernel of the ${\pi }_1$-shape group homomorphism determined by a general space $X$, and establish, for each locally path connected, paracompact Hausdorff space $X$, $\ker {\Psi }_X$ is precisely the Spanier group of $X$.

23 Pages, 1 figure, To appear in Rocky Mountain Journal of Mathematics