THE FINITENESS OBSTRUCTION FOR LOOP SPACES
Author: Dietrich Notbohm
AMS class.: 57Q12, 55R35, 55R10
Address: Mathematisches Institut
Universität Göttingen
Bunsenstr. 3-5
37073 Göttingen
Germany
e-mail: notbohm@cfgauss.uni-math.gwdg.de
For finitely dominated spaces, Wall constructed a finiteness obstruction,
which decides whether a space is equivalent to a finite $CW$-complex
or not.
It was conjectured that this finiteness obstruction always vanishes for
quasi finite $H$-spaces, that are $H$-spaces whose homology looks like the
homology of a finite $CW$-complex. In this paper we prove this conjecture for loop spaces. In particular, this shows that every quasi finite
loop space is actually homotopy equivalent to a finite $CW$-complex.