## The Relation of Cobordism to K-theories |

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should be noted that on the coefficient groups , -2n ۳۰ : 02 -2n - K ( pt ) = Z U U is identified up to sign with the

should be noted that on the coefficient groups , -2n ۳۰ : 02 -2n - K ( pt ) = Z U U is identified up to sign with the

**Todd genus**td : 12 - 2 . 2n In Chapter II we show among other things that the cobordism theories determine the K ...Page 37

The composition Mc -2n au ño ( pt ) → K ( pt ) = 2 ° 2n U maps a cobordism class [ manj of closed weakly complex manifolds into the integer ( -1 ) " td [ man ] , where td [ man ) is the

The composition Mc -2n au ño ( pt ) → K ( pt ) = 2 ° 2n U maps a cobordism class [ manj of closed weakly complex manifolds into the integer ( -1 ) " td [ man ] , where td [ man ) is the

**Todd genus**of Man as in Hirzebruch . 2n Proof .Page 66

commutes , hence hence B ' has Hcl B'en Using the -8n U isomorphism 12 0 C 22 the element [ Mon , e nu corresponding to U B'S has

commutes , hence hence B ' has Hcl B'en Using the -8n U isomorphism 12 0 C 22 the element [ Mon , e nu corresponding to U B'S has

**Todd genus**T [ Mon , = + 1 according to ( 6.5 ) . It is then sufficient to switch to bordism .### 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