Commentarii Mathematici Helvetici

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Volume 74, Issue 4, 1999, pp. 657–670
DOI: 10.1007/s000140050110

Published online: 1999-12-31

The finiteness obstruction for loop spaces

D. Notbohm[1]

(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