## The Relation of Cobordism to K-theories |

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0400510Y1 9 0 o ) ; a zero element is given by d ( 5 , 5 , l ) where § is any bundle over X. It is clear that addition is

0400510Y1 9 0 o ) ; a zero element is given by d ( 5 , 5 , l ) where § is any bundle over X. It is clear that addition is

**abelian**. It is not difficult to show the existence of negatives , so that the set of equivalence classes becomes ...Page 89

U Consider the free

U Consider the free

**abelian**group Hom ( 2n ° 4 ) of rank T ( n ) and let K C Hom ( m2 U , Z ) 2n = G Hence be the subgroup spanned by all the s as w varies over all partitions with diw ) ? n . Now G / K is clearly a finite**abelian**group ...Page 92

Denote the bordism class containing ma by [ M ] and denote the

Denote the bordism class containing ma by [ M ] and denote the

**abelian**group of bordism classes by a fr . The cartesian product of two stably framed manifolds is stably framed and for E sfr is a graded ring under cartesian product [ 12 ] ...### 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