A splitting theorem for connected moravaK-theories |
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Authors: | Rolf Kultze |
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Institution: | 1. Fachbereich Mathematik der Universit?t, Robert-Mayer-Str. 6-10, D-6000, Frankfurt/Main
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Abstract: | LetX be a connected, locally finite spectrum and letk(n) (n>-1) denote the (−1)-connected cover of then-th MoravaK-Theory associated to the primep.k(n) is aBP-module spectrum with π*(k(n)) ≅ ℤ
p
υ
n
] where |v
n
| = 2(p
n
-1). We prove the following splitting theorem: Thek(n)
*-torsion ofk(n)
* (X) is already annihilated byv
n
e
(e≥1) if and only ifk(n)ΛX is homotopy equivalent to a wedge of spectrak(n) and
r
k(n) (0≤r≤e-1) where
r
k(n) denotes ther-th Postnikov factor ofk(n). Moreover we investigate splitting conditions for
r
k(n)ΛX. |
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Keywords: | |
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