Bases for Cooperations in K-Theory

Clarke, Francis; Crossley, Martin D.; Whitehouse, Sarah

doi:10.1023/a:1011820819598

Cited by 19 publications

(54 citation statements)

References 12 publications

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“…Results of this sort can be found in [8,13,9,10]. We present a unifying framework encompassing these results and we also give some new examples.…”

Section: Introductionmentioning

confidence: 71%

“…As explained in [9], this is isomorphic to the ring K (p)0 (k (p) ) of degree zero stable cooperations in p-local complex K-theory.…”

Section: Examples Related To K-theory Operationsmentioning

confidence: 98%

“…The first example below is classical and is related to additive unstable operations in K-theory, as explained in [8,13]. Examples (4.2) and (4.3) relate to stable operations, and these bases were presented in [9,10]. The bases given in examples (4.4) and (4.5) relate to additive unstable operations, this time in the p-local setting, and these are new.…”

Section: Examples Related To K-theory Operationsmentioning

confidence: 99%

“…For p = 2, the same procedure carried out with the sequence α i = (−1) i 3 i/2 yields a topological basis for K 0 (2) (K (2) ). This basis is new-the periodic 2-local case was omitted from [10]. (KO (2) ).…”

Section: Integer-valued Polynomials and K-theory Operations 2231mentioning

confidence: 99%

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Integer-valued polynomials and $K$-theory operations

Strong

Whitehouse

2010

Proc. Amer. Math. Soc.

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Abstract. This paper provides a unifying approach to recent results linking the fields of integer-valued polynomials and operations in K-theory. Following work of Bhargava, we set up a general framework encompassing several examples of rings of integer-valued polynomials. Our main results give bases for the duals of these rings. The rings and their duals all arise in topology as various kinds of cooperations and operations in complex K-theory. We show how several previously understood examples fit into this framework and we present some new examples.

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“…Results of this sort can be found in [8,13,9,10]. We present a unifying framework encompassing these results and we also give some new examples.…”

Section: Introductionmentioning

confidence: 71%

“…As explained in [9], this is isomorphic to the ring K (p)0 (k (p) ) of degree zero stable cooperations in p-local complex K-theory.…”

Section: Examples Related To K-theory Operationsmentioning

confidence: 98%

Section: Examples Related To K-theory Operationsmentioning

confidence: 99%

Section: Integer-valued Polynomials and K-theory Operations 2231mentioning

confidence: 99%

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Integer-valued polynomials and $K$-theory operations

Strong

Whitehouse

2010

Proc. Amer. Math. Soc.

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“…This paper builds on recent work on stable operations in p-local complex K-theory [5]. That work described all operations in terms of Adams operations.…”

Section: Introductionmentioning

confidence: 99%

Infinite sums of Adams operations and cobordism

Gálvez

Whitehouse

2005

Math. Z.

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Abstract. In recent work, various algebras of stable degree zero operations in p-local K-theory were described explicitly [5]. The elements are certain infinite sums of Adams operations. Here we show how to make sense of the same expressions for M U (p) and BP , thus identifying the "Adams subalgebra" of the algebras of operations. We prove that the Adams subalgebra is the centre of the ring of degree zero operations.

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Stable Homotopy Theory, Formal Group Laws, and Integer-Valued Polynomials

Johnson

2014

Commutative Algebra

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Bases for Cooperations in K-Theory

Abstract: Abstract. Gaussian polynomials are used to define bases with good multiplicative properties for the algebra K * (K) of cooperations in K-theory and for the invariants under conjugation.

Cited by 19 publications

References 12 publications

Integer-valued polynomials and $K$-theory operations

Integer-valued polynomials and $K$-theory operations

Infinite sums of Adams operations and cobordism

Stable Homotopy Theory, Formal Group Laws, and Integer-Valued Polynomials

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