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Proceedings of the Edinburgh Mathematical Society (1)

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Central Cohomology Operations and K-Theory
Imma Gálvez-Carrillo, Sarah Whitehouse
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 57 / Issue 3 / October 2014

Published online by Cambridge University Press:

16 April 2014, pp. 699-711
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For stable degree 0 operations, and also for additive unstable operations of bidegree (0, 0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresponding ring of connective complex K-theory operations. Similarly, the centre of the ring of BP operations is the corresponding ring for the Adams summand of p-local connective complex K-theory. Here we show that, in the additive unstable context, this result holds with BP replaced by BP〈n⌰ for any n. Thus, for all chromatic heights, the only central operations are those coming from K-theory.