Unstable K-cohomology Algebra Is Filtered Λ-ring
نویسنده
چکیده
Boardman, Johnson, and Wilson (1995) gave a precise formulation for an unstable algebra over a generalized cohomology theory. Modifying their definition slightly in the case of complex K-theory by taking into account its periodicity, we prove that an unstable algebra for complex K-theory is precisely a filtered λ-ring and vice versa. 1. Introduction. Lambda operations in complex K-theory were first introduced by Grothendieck. These operations should be thought of as exterior power operations; in fact, for an element α in K(X) that comes from an actual vector bundle on X with X a finite complex, λ i (α) is the element represented
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Unstable K-cohomology Algebra Is Filtered Lambda-ring
Boardman, Johnson, and Wilson gave a precise formulation for an unstable algebra over a generalized cohomology theory. Modifying their definition slightly in the case of complex K-theory by taking into account its periodicity, we prove that an unstable algebra for complex K-theory is precisely a filtered λ-ring, and vice versa.
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