## The Relation of Cobordism to K-theories |

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trying to make it clear in each case . n

trying to make it clear in each case . n

**Naturally**we may also use ( 7.6 ) . We have MU ( 1 ) = CP ( 00 ) . Thus 2 i : CP ( n ) CCP ( C ) yields an elemento ( CP ( n ) ) . Then ( 7.6 ) applies to prove the following : ( 8.3 ) COROLLARY ...Page 59

( X , A ) over the module 0 * In fact , K * ( X , A ) = n * ( x , A ) ® * Z where 2 is a ( * -ring in a Ω ,

( X , A ) over the module 0 * In fact , K * ( X , A ) = n * ( x , A ) ® * Z where 2 is a ( * -ring in a Ω ,

**natural**way . In a similar fashion , n * ( X , A ) determines Ko * ( x , A ) . There is the homomorphism Mc : ng = z ; thus for ...Page 71

admits such a

admits such a

**natural**operator J , then mh receives a**natural**To : R2 o U - structure . Thus every almost complex manifold and hence every complex analytic manifold also has a**natural**U - structure . A U - manifold ( M " , ) is a pair ...### 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