## The Relation of Cobordism to K-theories |

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Page 36

ch Mold ) = f * ch = f * ch 5K 15 ) = ptop - ch 115 ) = f * P ( S ) P ( S ) = S ( 2 ) . k 长* We now consider -2n Me : ( pt ) K ° ( pt ) = Z. U Note that 2 -2n ( pt ) = 2-2n ( so ) [ s2n + 25 ,

ch Mold ) = f * ch = f * ch 5K 15 ) = ptop - ch 115 ) = f * P ( S ) P ( S ) = S ( 2 ) . k 长* We now consider -2n Me : ( pt ) K ° ( pt ) = Z. U Note that 2 -2n ( pt ) = 2-2n ( so ) [ s2n + 25 ,

**MU**(**K**) ] . U U 7 may f : k Suppose now ...Page 97

f ~ ( El 5k ) , F ) ( E ( 7 ) , E17 ) OM ) ) 7 ( м , ам ) f ( BU ( K ) , xo ) Passing to disk bundles , we may ... Composing these , we get from many a map sh + 2k →

f ~ ( El 5k ) , F ) ( E ( 7 ) , E17 ) OM ) ) 7 ( м , ам ) f ( BU ( K ) , xo ) Passing to disk bundles , we may ... Composing these , we get from many a map sh + 2k →

**MU**(**K**) / s2k thus an element of TT n + 2k (**MU**(**K**) / s2k ) ...Page 98

H2n ( BU ( k ) ) = # 2n + 2K (

H2n ( BU ( k ) ) = # 2n + 2K (

**MU**(**k**) ) + H2n + 2k ( s2n + 2k 个 80 * q * 2n + 2k 2k H (**MU**(**K**) / S " ) . * * .1 The image ga gloi ,. •• C1y ) , 11 + --- + ix = n , are invariants of the homo topy class of g .### 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