## The Relation of Cobordism to K-theories |

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Page 29

( 5.2 ) For each finite CW complex X with base point , commutativity

( 5.2 ) For each finite CW complex X with base point , commutativity

**holds**in KU * ( x ) = KO ( s * x ) 4 Ma Õ ( X ) Ms 10 SU KSP ( X ) where $ 17 ) = 11 - 57 ) ® 7 with 5 , the Hopf Sp ( 1 ) -bundle over 54 . Proof .Page 46

Suppose that is an Sp ( m ) -bundle over X , and that uniqueness

Suppose that is an Sp ( m ) -bundle over X , and that uniqueness

**holds**for Sp ( n ) -bundles , n < m . There is the associated sphere bundle $ 4m - 1 * * S ( 5 ) - → X ; moreover Sp ( l ) , the unit sphere of quaternions , acts freely ...Page 51

... well define that Pk ( 5 ) as elements of a ( x ) . SU In fact Sp ( 1 ) 4 SU ( 2 ) so we could also consider Pm € 2 SU ( HP ( n ) ) . Clearly ( 8.1 )

... well define that Pk ( 5 ) as elements of a ( x ) . SU In fact Sp ( 1 ) 4 SU ( 2 ) so we could also consider Pm € 2 SU ( HP ( n ) ) . Clearly ( 8.1 )

**holds**for a so that ( 7.5 )**holds**in that case . natural map 12 ( :) ( • ) maps the ...### 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