## The Relation of Cobordism to K-theories |

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denote by [ X , Mnd the

denote by [ X , Mnd the

**homotopy**classes of base point preserving maps X - > Mni Given f : X > Mne there is the composition sta л х Mh which we also denote by Sf : S s ? 1 X - M Define → M Mat1 n + lo in ( X ; M ) = Dir Lim isk 1 X ...Page 105

Such a ( U , SU ) -structure induces a natural SU - structure on OBh of Note that the cross - section of U > on induces a principal U ( 1 ) -bundle over B , which along 9 Bh already has a

Such a ( U , SU ) -structure induces a natural SU - structure on OBh of Note that the cross - section of U > on induces a principal U ( 1 ) -bundle over B , which along 9 Bh already has a

**homo topy**class of cross - sections ; thus , the ...Page

A. Liulevicious , Notes on

A. Liulevicious , Notes on

**homo topy**of Thom spectra , Amer . J. Math . 86 , 1 - 16 ( 1964 ) . ... J. W. Milnor and M. A. Kervaire , Bernoulli numbers ,**homotopy**groups , and a theorem of Rohlin , Proc . Int . Cong . Math .### 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