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Sep, 2019
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Chromatic Phenomena in Unstable Homotopy Theory

In modern stable homotopy theory , it is an important technique to decompose homotopy theoretic informations into v n -periodic informations by using BP -theory .

In unstable homotopy theory, on the other hand, we know the v 0 -periodic informations algebraically as rational homotopy theory . The v 1 -periodic homotopy groups are studied by D. Davis and others, but we don’t have a systematic treatment which can be called v 1 -periodic homotopy theory. Compared to stable homotopy theory, we are still in the era before Ravenel published his conjectures.

In unstable homotopy, we need to study not only periodic informations but also torsion informations, as is suggested by the study of exponents by Cohen, Moore, and Neisendorfer .