## The Relation of Cobordism to K-theories |

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Page 4

If n = 4k + 2 then av becomes a right

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**quaternionic**linear fashion .Page 5

using ( 1.4 ) , so that SU ( n ) acts in a

using ( 1.4 ) , so that SU ( n ) acts in a

**quaternionic**linear fashion . If n = 4k , we have pa = 1 . Hence Av = RV R_ ( V ) . If X E RV , then ph ( Xi ) = -1 pe X ) 1 = -X1 and Xi E R_ ( V ) . The theorem is then proved .Page 14

galleg , 8V , xx ) ) = ( ( eg - , & v , Pey ( BY ) ) ) ( leg- , 8V , 8 g ( Y ) ) ) by ( 2.5 ) Pile , v , y ) ) . ev ( 3.2 ) If is an su ( n ) - bundle over X , n = 4k + 2 , then we have

galleg , 8V , xx ) ) = ( ( eg - , & v , Pey ( BY ) ) ) ( leg- , 8V , 8 g ( Y ) ) ) by ( 2.5 ) Pile , v , y ) ) . ev ( 3.2 ) If is an su ( n ) - bundle over X , n = 4k + 2 , then we have

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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