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UBC Theses and Dissertations
Adams operations on KO(X) ⊕ KSp (X) Allard, Jacques
Abstract
Let KO(X) be the real and KSP(X) be the quaternionic K-theory of a finite CW-complex X . The tensor product and the exterior powers of vector bundles induce on
L(X) = KO(X) ⊕ KSP(X) the structure of Z₂ -graded λ-ring.
In this thesis it is shown, that the Adams operations
Ѱk : L(X) → L(X) , k = l, 2, 3,...,
which are associated to this λ-ring, are ring homomorphisms and satisfy the composition law
Ѱk ₀ Ѱℓ = Ѱℓk = Ѱℓ ₀ Ѱk , k, ℓ = 1, 2, 3,...
Finally, the ring L(X) together with its Ѱ-operations is explicitely determined for the quaternionic and complex projective spaces.
Item Metadata
| Title |
Adams operations on KO(X) ⊕ KSp (X)
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
1973
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| Description |
Let KO(X) be the real and KSP(X) be the quaternionic K-theory of a finite CW-complex X . The tensor product and the exterior powers of vector bundles induce on
L(X) = KO(X) ⊕ KSP(X) the structure of Z₂ -graded λ-ring.
In this thesis it is shown, that the Adams operations
Ѱk : L(X) → L(X) , k = l, 2, 3,...,
which are associated to this λ-ring, are ring homomorphisms and satisfy the composition law
Ѱk ₀ Ѱℓ = Ѱℓk = Ѱℓ ₀ Ѱk , k, ℓ = 1, 2, 3,...
Finally, the ring L(X) together with its Ѱ-operations is explicitely determined for the quaternionic and complex projective spaces.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2011-03-22
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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| DOI |
10.14288/1.0080120
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| URI | |
| Degree (Theses) | |
| Program (Theses) | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Campus | |
| Scholarly Level |
Graduate
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| Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.