Miller Spaces and Spherical Resolvability of Finite Complexes

Details Miller Spaces and Spherical Resolvability of Finite Complexes Miller Spaces and Spherical Resolvability of Finite Complexes

2001-11-13

arxiv.org/abs/math/0111151v1

Mathematics

Algebraic Topology

9 pages

Scientific paper

We show that if $K$ is a nilpotent finite complex, then $\Omega K$ can be
built from spheres using fibrations and homotopy (inverse) limits. This is
applied to show that if ${\mathrm {map}}_*(X,S^n)$ is weakly contractible for
all $n$, then ${\mathrm {map}}_*(X,K)$ is weakly contractible for any nilpotent
finite complex $K$.

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