## The Relation of Cobordism to K-theories |

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Page 21

We thus have the following

We thus have the following

**corollary**. ( 4.3 )**COROLLARY**. The Sp ( 1 ) -bundle 3 over HP ( n - l ) has Thom n - l space HP ( n ) , and 315 ) = 1 5 in KSp ( HP ( n ) ) . n - 1 n Naturally , entirely similar results hold for complex line ...Page 37

( 6.5 )

( 6.5 )

**COROLLARY**. The composition Mc -2n au ño ( pt ) → K ( pt ) = 2 ° 2n U maps a cobordism class [ manj of closed weakly complex manifolds into the integer ( -1 ) " td [ man ] , where td [ man ) is the Todd genus of Man as in ...Page 57

... A ) have y por KP ) for for every 78 E KO ( X , A ) , for any finite pair ( X , A ) . Consider the diagram Proof . Po KO ( x ) ño ( x ) M Sp ᅨ 88 88 KO4 ( s4 - x ) < 224 ( s 1 x ) Sp F al P1 기 KSP ( S x ) 1 id .

... A ) have y por KP ) for for every 78 E KO ( X , A ) , for any finite pair ( X , A ) . Consider the diagram Proof . Po KO ( x ) ño ( x ) M Sp ᅨ 88 88 KO4 ( s4 - x ) < 224 ( s 1 x ) Sp F al P1 기 KSP ( S x ) 1 id .

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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