## The Relation of Cobordism to K-theories |

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Page 4

**Consider**the complex inner product space v of dimension n , with given su - structure CE i MV . If n = 4k + 2 then av becomes a right quaternionic vector space by defining Y.j K ( Y ) for Y E Av . Moreover su ( n ) acts on 1v in a ...Page 7

**Consider**then R RV RW → AV 1W = R с 1 ( v + W ) which by ( 2.2 ) has image in R ( V + W ) . It is seen that if y E Kernel 8 , then 11 15y = - ( 11 ) y . If also y E R ( V ) R R ( W ) then the left hand side belongs to R R_ ( V ) R R ...Page 55

As promised , we now

As promised , we now

**consider**M : * ( . ) → Ko * ( • ) , the comSp position * ) - Sp THEOREM . 4k 4k ( 9.3 ) Let 5 denote an Sp ( m ) -bundle over a finite CW complex X , and let Pk15 ) en Sp ( x ) and õ ( 5 ) € KO ( x ) be the classes ...### 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