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.
Keywords : condition $ (T^{\ast \ast})$, (locally) nilpotent space, solvable space, homotopy equivalence
MSC numbers : Primary 55N10; Secondary 55N91
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