Abstract.
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.
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Received: March 25, 1999.
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Notbohm, D. The finiteness obstruction for loop spaces. Comment. Math. Helv. 74, 657–670 (1999). https://doi.org/10.1007/s000140050110
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DOI: https://doi.org/10.1007/s000140050110