Commentarii Mathematici Helvetici
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Published online: 1999-12-31
The finiteness obstruction for loop spacesD. Notbohm (1) Universität Göttingen, Germany
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.
Keywords: Finiteness obstruction, Wall obstruction, loop space, p-compact group
Notbohm D.: The finiteness obstruction for loop spaces. Comment. Math. Helv. 74 (1999), 657-670. doi: 10.1007/s000140050110