## The Relation of Cobordism to K-theories |

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U , fr 2n → 12 fr 2n - 1 2n Td Q which

U , fr 2n → 12 fr 2n - 1 2n Td Q which

**gives**rise to a homomorphism fr E y : - > Q / z . 2n - 1 This turns out to coincide with a well - known homomorphism of Adams , : fr 2n - 1 → Q / 2 . We are thus able to**give**a cobordism ...Page 47

n i = 0 Upon restriction to U this

n i = 0 Upon restriction to U this

**gives**zero . Also consider Σ E i = 0 Since HP ( 5 @p UUV , one sees that ( -1 ) ) T * ( P367 ) ) pn - J , which upon restriction to v**gives**zero . B ( Σ i = 0 = 0 in h * ( HP ( 5 ( -1 ) 4 77 * ( P ...Page 97

We could

We could

**give**a complete bordism description of this group , but we forego the tedious details . Given an man , n > 0 , and the associated map 8 : s2n + 2k → MU ( K ) / s2k , there is H2n ( BU ( k ) ) = # 2n 97.### 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