## The Relation of Cobordism to K-theories |

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Page 69

U - MANIFOLDS WITH

U - MANIFOLDS WITH

**FRAMED**BOUNDARIES In this chapter we shift from our very general point of view of the previous ... classes [ M ] of closed differentiable manifolds n with a given complex structure on the**stable**tangent bundle .Page 91

U - manifolds with

U - manifolds with

**stably framed**boundaries . 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 ...Page 92

One can then define a bordism relation on closed

One can then define a bordism relation on closed

**stably framed**manifolds by My ~ ven if there exists a compact**stably framed**manifold whtl with owntl the disjoint union M V ( -M ) as**stably framed**manifolds . Denote the bordism class ...### 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