## The Relation of Cobordism to K-theories |

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Page 49

For example the coefficient

For example the coefficient

**ring**( * has ( -2n anu the cobordism group of closed weakly U U 2n * complex manifolds of dimension 2n . Hence a is a polynomial**ring**U over the integers with one generator in each dimension -2n ( Milnor ( 19 ) ...Page 59

In this section we improve upon the results of * * U * * U U Sp → kan section 9 by showing how to construct the 22 - graded

In this section we improve upon the results of * * U * * U U Sp → kan section 9 by showing how to construct the 22 - graded

**ring**Ko ( X , A ) knowing only the graded algebra 2. ( X , A ) over the module 0 * In fact , K * ( X , A ) = n ...Page 66

SU Pon is not a divisor of zero in the

SU Pon is not a divisor of zero in the

**ring*** -on Proof . The proof is based on our previous paper [ 12 ] . First we According have to convert the statement to one in terms of bordism . to section 5 , 2. ( . ) SU x1 on -8n E no + 1 .### 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 | |

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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