## The Relation of Cobordism to K-theories |

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... 3 ) ^ X , there exist isomorphisms letting sx denote the suspension s ? ñ * ( x ) ~ ñ 1 + 1 ( sx ) such that if f : X → Y then

... 3 ) ^ X , there exist isomorphisms letting sx denote the suspension s ? ñ * ( x ) ~ ñ 1 + 1 ( sx ) such that if f : X → Y then

**commutativity**holds in mnt ( y ) > 71 + 2 ( SY ) J J f * ( Sf ) * m * ( x ) as ñ + 1 ( sx ) .Page 29

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

( 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 107

If we also define a SU , fr we obtain a

If we also define a SU , fr we obtain a

**commutative**diagram + 1/2 . Since = 1 n 1 U , SU nul 2 SU n SU , fr a n ( Մ ج QU , f - nfr n n n - l U , SU 0 SU 22 n - 1 n : where the two vertical sequences and the two hroizontal are both ...### 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