Generalized cohomology of pro-spectra

Details Generalized cohomology of pro-spectra Generalized cohomology of pro-spectra

2004-08-13

arxiv.org/abs/math/0408179v1

Mathematics

Algebraic Topology

Scientific paper

We present a closed model structure for the category of pro-spectra in which the weak equivalences are detected by stable homotopy pro-groups. With some bounded-below assumptions, weak equivalences are also detected by cohomology as in the classical Whitehead theorem for spectra. We establish an Atiyah-Hirzebruch spectral sequence in this context, which makes possible the computation of topological K-theory (and other generalized cohomology theories) of pro-spectra.

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