## The Relation of Cobordism to K-theories |

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Page 19

Form the join E ( 5 ) • Sp ( l ) , and

Form the join E ( 5 ) • Sp ( l ) , and

**denote**its < < points by 11 - t ) e + th where u t l , e E ( 5 ) , he Sp ( l ) . Then a principal action of Spll ) is given by ( ( 1 t ) e + th ) g = ( 1 t ) eg + töng .Page 26

**denote**by [ X , Mnd the homotopy classes of base point preserving maps X - > Mni Given f : X > Mne there is the composition sta л х Mh which we also**denote**by Sf : S s ? 1 X - M Define → M Mat1 n + lo in ( X ; M ) = Dir Lim isk 1 X ...Page 75

The Atiyah classes of this complex vector space bundle are

The Atiyah classes of this complex vector space bundle are

**denoted**simply by r . ( MM € K ( M " ) ; similarly there are the classes s ( MA ) K ( M " ) . ...**Denote**by the conjugate of the Hopf bundle over CP ( n ) .### 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