## The Relation of Cobordism to K-theories |

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Page 22

over a 2 - In

over a 2 - In

**particular**, ( 4.4 ) The Hopf U ( 1 ) -bundle n - 1 over CP ( n 1 ) has Thom space CP ( n ) , and TlS n - 1 ' = 1 - Sn in K ( CP ( n ) ) . If we apply ( 4.4 ) to the trivial complex line bundle so point , then 219 ) é ř ...Page 63

coefficient group , we get a ring homomorphism pints * → KO = KO “ ( pt ) * In

coefficient group , we get a ring homomorphism pints * → KO = KO “ ( pt ) * In

**particular**we can consider Ko as a left 12 - module , letting Sp Woo = Mlwood for wen * and KE KO * . Sp We thus obtain a homomorphism KR1 n $ p x , KO * KO ...Page 64

It is convenient to choose a

It is convenient to choose a

**particular**model for BSp ( n ) . Namely let M denote all n - dim . quaternionic subspaces of an N - dim . quaternionic space , N large , and take n , N BSp ( n ) = M Mnen We then need that a basis for the Z ...### 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