On Homotopy Equivalence of Nonnilpotent Spaces and Its Applications
Commun. Korean Math. Soc. 2000 Vol. 15, No. 2, 349-355
Sang-Eon Han Honam University
Abstract : In this paper we generalize the Whitehead theorem which says that a homology equivalence implies a homotopy equivalence for nilpotent spaces. We make some theorems on a homotopy equivalence of non-nilpotent spaces, e.g., the solvable space or space satisfying the condition $(T^{\ast \ast})$ or space $X$ with $\pi_1(X)$ Engel, or locally nilpotent space with some properties. Furthermore we find some conditions that the Wall invariant will be trivial.
