## The Relation of Cobordism to K-theories |

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The

The

**coefficient**groups are , taking one case U U , an ( point ) , 02 U U n U U related by Moreover is just the bordism group of all U bordism classes ( Mn ) of closed weakly almost complex manifolds mh , SU similarly for a On the other ...Page 49

For example the

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 80

We assume the fact ( see Hirzebruch ( 16 ) ) that the

We assume the fact ( see Hirzebruch ( 16 ) ) that the

**coefficient**of th in the above is one , and thus that Td ( CP ( n ) ) = 1 . ( 1 - Bjk where P is the Hopf bundle and on ? ch x • T ( CP ( n ) ) ( 1 - e - tjk ( t / ( 1 - e - ty ) tk ...### 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