## The Relation of Cobordism to K-theories |

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Page 7

If m = 4k and n = 4 % + 2 then one sets up

If m = 4k and n = 4 % + 2 then one sets up

**similarly**an isomorphism RV W 1W ~ 1 ( V + w ) of quaternionic vector spaces , where q E H acts R on the left hand side by 10 ...Page 18

If 5 is an SU ( mm ) -bundle and 7 an SU ( n ) -bundle , we have

If 5 is an SU ( mm ) -bundle and 7 an SU ( n ) -bundle , we have

**similarly**t ( 5 * 7 ) = m = t15 ) x tlp ) , n = 4k , n = 4 / s ( n t ( 5 ) x 817 ) , m = 4k , n = 42 + 2 t ( 3 X n ' s ( 5 ) x slp ) , n = 4k + 2 , n = 42 + 2 . ) = 4 .Page 76

Recall also that there is the ordinary Thom isomorphism 0 : : ** ( X , A ) — # k + 2n ( D ( 5 ) , D ( 3A ) U S ( 3 ) on cohomology ;

Recall also that there is the ordinary Thom isomorphism 0 : : ** ( X , A ) — # k + 2n ( D ( 5 ) , D ( 3A ) U S ( 3 ) on cohomology ;

**similarly**on homology there is 9 : H ( X , A ) = Htan ( D ( 5 ) , D ( 3A ) US ( 5 ) ) . nev ...### 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