Free abelian topological groups and collapsing maps

https://doi.org/10.1016/j.topol.2011.03.019Get rights and content
Under an Elsevier user license
open archive

Abstract

We show that for every pair (X,Y) of ANR compacta, YX, the free abelian topological group applied to a collapsing map q:XX/Y produces a locally trivial bundle A(q):A(X)A(X/Y) with the fiber A(Y). As a result we obtain a short proof of the classical Dold–Thom theorem which states that H˜n(X)=πn(A(X)) for all complexes X.

MSC

primary
54H11
55R10
secondary
54C55
55N40

Keywords

Free abelian topological group
Fibration
Homology
Dold–Thom theorem

Cited by (0)

1

Supported by NSF, grant DMS-0904278.