## The Relation of Cobordism to K-theories |

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Page 69

In section 12 we consider the bordism group 2 of closed U - manifolds of dimension n ; the elements of nu are the bordism classes [ M ] of closed differentiable manifolds n with a given complex structure on the

In section 12 we consider the bordism group 2 of closed U - manifolds of dimension n ; the elements of nu are the bordism classes [ M ] of closed differentiable manifolds n with a given complex structure on the

**stable tangent bundle**.Page 91

Let M denote a differentiable manifold and let I denote its tangent bundle . Denote as usual the

Let M denote a differentiable manifold and let I denote its tangent bundle . Denote as usual the

**stable tangent bundle**of Ma to be T + ( 2k n where 2k - n ? 2 . A stable framing e of Mh is a homo topy class of maps 9 : El T + ( 2k 2k n ) ...Page 93

Picking representatives of $ and e , we may regard the

Picking representatives of $ and e , we may regard the

**stable tangent bundle**? + ( 2k- n ) as a complex vector space bundle on ma with a given trivialization , as a complex vector space bundle , when restricted to om .### 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