## The Relation of Cobordism to K-theories |

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Page 18

Thom classes of

Thom classes of

**line bundles**. Suppose that gis an SU ( 2 ) -bundle over a finite complex X ; according to section 3 we receive an element s ( 5 ) E KSP ( M ( 5 ) ) . A purpose of this section is to compute s ( x ) .Page 20

I go ( W ) = 9,18- * • w ) for 8 € Sp ( 1 ) . Now yeri 5 ' ) is the trivial quaternionic

I go ( W ) = 9,18- * • w ) for 8 € Sp ( 1 ) . Now yeri 5 ' ) is the trivial quaternionic

**line bundle**over D ( 5 ) ; let i denote the trivial quaternionic**line bundle**over E ( 5 ) . Sp ( 1 ) / Sp ( l ) . There is the bundle map Finer ( 3 ) ...Page 34

A standard splitting argument shows that r ( 5 ) u ( 5 ) for all F if it is true for universal

A standard splitting argument shows that r ( 5 ) u ( 5 ) for all F if it is true for universal

**line bundles**. over CP ( n ) . by ( 4.3 ) . Hence ) = 1 and n + 1 ) = 1 Consider then the Hopf complex**line bundle**S We have M ( Sn ) = CP ...### 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