## The Relation of Cobordism to K-theories |

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denote by [ X , Mnd the homotopy classes of base point preserving maps X - > Mni Given f : X > Mne there is the

denote by [ X , Mnd the homotopy classes of base point preserving maps X - > Mni Given f : X > Mne there is the

**composition**sta л х Mh which we also denote by Sf : S s ? 1 X - M Define → M Mat1 n + lo in ( X ; M ) = Dir Lim isk 1 X ...Page 29

fine Ms \ ß to be the image of s under the

fine Ms \ ß to be the image of s under the

**composition**4k + 2 f ' KSP ( MSU ( 4k + 2 ) ) KSP ( 58k 1 x ) KSP ( x ) . ( 5.2 ) For each finite CW complex X with base point , commutativity holds in KU * ( x ) = KO ( s * x ) 4 Ma Õ ( X ) Ms ...Page 60

K * ( X , A ) → 1 * ( X , A ) , Å the

K * ( X , A ) → 1 * ( X , A ) , Å the

**composition**K TM ( X , A ) ( X , A ) 1 * ( x , A ) . Moreover the * ***composition**Ê À , x * ( 4,4 ) K ^ ( X , A ) n * ( X , A ) → K * ( x , A ) 11 has ad id . ( 10.1 ) THEOREM .### 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