The finiteness obstruction for loop spaces

Authors
Citation
D. Notbohm, The finiteness obstruction for loop spaces, COMM MATH H, 74(4), 1999, pp. 657-670
Citations number
31
Categorie Soggetti
Mathematics
Journal title
COMMENTARII MATHEMATICI HELVETICI
ISSN journal
00102571 → ACNP
Volume
74
Issue
4
Year of publication
1999
Pages
657 - 670
Database
ISI
SICI code
0010-2571(1999)74:4<657:TFOFLS>2.0.ZU;2-W
Abstract
For finitely dominated spaces, Wall constructed a finiteness obstruction, w hich decides whether a space is equivalent to a finite CW-complex or not. I t was conjectured that this finiteness obstruction always vanishes for quas i 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 sp aces. In particular, this shows that every quasi finite loop space is actua lly homotopy equivalent to a finite CW-complex.