The Relation of Cobordism to K-theories |
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Page 11
Application to bundles . In this section the constructions of the preceding sections are applied to U ( n ) -bundles and SU ( n ) -bundles . For example , given an SU ( 2k ) -bundle § there are associated two real vector space bundles ...
Application to bundles . In this section the constructions of the preceding sections are applied to U ( n ) -bundles and SU ( n ) -bundles . For example , given an SU ( 2k ) -bundle § there are associated two real vector space bundles ...
Page 12
Replacing Av by 1 odvi , nervi respectively in the above , we obtain bundles od 1 ( 5 ) → X and 1 ( E ) > X. ev If ... If n = 0 mod 4 , we get a real vector space bundle R ( 3 ) → X , where R ( E ) = = { x Alternatively , x : x6115 ) ...
Replacing Av by 1 odvi , nervi respectively in the above , we obtain bundles od 1 ( 5 ) → X and 1 ( E ) > X. ev If ... If n = 0 mod 4 , we get a real vector space bundle R ( 3 ) → X , where R ( E ) = = { x Alternatively , x : x6115 ) ...
Page 13
In the above , given vector space bundles o → X and Y Y we mean by p By → X X Y the vector space bundle whose fiber above ( x , y ) is p - ' ( x ) » -f ( y ) . Also in cases 1 and 4 , the two bundles are equivalent as real vector ...
In the above , given vector space bundles o → X and Y Y we mean by p By → X X Y the vector space bundle whose fiber above ( x , y ) is p - ' ( x ) » -f ( y ) . Also in cases 1 and 4 , the two bundles are equivalent as real vector ...
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Contents
CONTENTS 1 | 1 |
Tensor products of exterior algebras | 5 |
Application to bundles | 11 |
Copyright | |
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Common terms and phrases
abelian According acts Adams assigning associated base point basis bordism bordism classes BSp(n Chapter characteristic Chern classes Chern numbers classes closed U-manifold cobordism coefficient commutativity compact U,fr)-manifold complex vector space composition consider construction COROLLARY CP(n define definition denote diagram dimension element equivalence exact exists fact fiber finite CW complex follows function give given Hence holds homo topy homomorphism HP(n identified induced integer isomorphism K-theory KSP(X line bundle linear manifold Moreover MU(K Namely natural Note obtain particular partition polynomial Proof prove quaternionic represented respectively ring seen Similarly stable tangent bundle stably framed structure su(n sufficient Suppose theorem Thom Todd genus trivial U-structure U,fr U(n)-bundle unique universal vector space bundle
Bibliographic information
| Title | The Relation of Cobordism to K-theories Volume 28 of Lecture notes in mathematics, ISSN 0075-8434 Relation of Cobordism to K-theories, Pierre E. Conner |
| Authors | Pierre E. Conner, E. E. Floyd |
| Publisher | Springer-Verlag, 1966 |
| ISBN | 0387036105, 9780387036106 |
| Length | 110 pages |
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