## The Relation of Cobordism to K-theories |

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Page 44

Hence dj , ... , dn is a basis and the theorem holds in case the fibring is

Hence dj , ... , dn is a basis and the theorem holds in case the fibring is

**trivial**. Consider next the general case . Let x ' be a subcomplex of X 1 - . and let E ! = TT ( X ' ) . Let M be a free h - module with basis ch ..... ch ...Page 45

Hence By the five lemma , if Yai Tz and Ta are isomorphism so is 71 if T , is an isomorphism and if E ' → X " ' is

Hence By the five lemma , if Yai Tz and Ta are isomorphism so is 71 if T , is an isomorphism and if E ' → X " ' is

**trivial**( so that E ' n Erl - X ' nxi is also**trivial**) , then , is an isomorphism . ' ' ) The theorem then follows ...Page 67

If f : x → søn → ñ * ( x ) is non -

If f : x → søn → ñ * ( x ) is non -

**trivial**1f and only if f → KO ( x ) is non -**trivial**. THEOREM . * søn then ñ * ( s8n ) : SU SU : KO ( sen , Proof . Consider the diagram 8n ( san , f * ã o SU Now SU ã on ģen ( x ) su va pl SUM KO ...### 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