## The Relation of Cobordism to K-theories |

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Page 39

In this section we state and prove a

In this section we state and prove a

**theorem**of Dold [ 13 ] which generalizes to an arbitrary multiplicative cohomology theory the ... uniqueness and existence**theorems**for characteristic classes of quaternionic and complex bundles .Page 42

The following

The following

**theorem**can be proved just as was a similar**theorem**in our previous work ( 10 ) . ( 7.3 )**THEOREM**. Let hl . ) be a multiplicative cohomology theory . Also let X and Y be finite CW complexes such that h ( y ) is a free h ...Page 45

The

The

**theorem**then follows readily . 1 We use Dold's**theorem**as a basic device in constructing characteristic classes . The following two**theorems**give the generalities . ( 7.5 )**THEOREM**. Let hl . ) be a multiplicative cohomology theory ...### What people are saying - Write a review

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### Contents

CONTENTS 1 | 1 |

Tensor products of exterior algebras | 5 |

Application to bundles | 11 |

Copyright | |

16 other sections not shown

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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