The finiteness obstruction for loop spaces | Zendy

Dietrich Notbohm | Zendy

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The finiteness obstruction for loop spaces

Author(s) -

Dietrich Notbohm

Publication year - 1999

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140050110

Subject(s) - mathematics , homotopy , loop space , homology (biology) , pure mathematics , loop (graph theory) , conjecture , cw complex , space (punctuation) , combinatorics , algebra over a field , cellular homology , biochemistry , chemistry , linguistics , philosophy , gene

. 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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