## The Relation of Cobordism to K-Theories |

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P. E. Conner, E. E. Floyd. Pierre E. Conner E. E. Floyd The Relation of Colbordism to K-Theories %) Springer Lecture

P. E. Conner, E. E. Floyd. Pierre E. Conner E. E. Floyd The Relation of Colbordism to K-Theories %) Springer Lecture

**Notes**in Mathematics A collection of informal reports and. Front Cover. Page

Lecture

Lecture

**Notes**in Mathematics A collection of informal reports and seminars Edited by A. Dold, Heidelberg and B. Eckmann, Zürich 28 P. E. Conner . E.E. Floyd University of Virginia, Charlottesville The Relation of Cobordism to K-Theories ... Page vii

**Note**that if m is even then A = /*1 (3) A 2. We consider now the proof of (2.l.) for m = 4k and n = 41. There is a natural homomorphism * : A W © Aw -> AW ... Page viii

... this is an anti-automorphism of H. There is a natural epimorphism x - AW & A W — /\W & A W. If X e Av and Y e AW, then o' maps /(X Goc Y) and X& Y into the /*(X (96 y) = A1x &c. Ae y = x3. same value. For we have

... this is an anti-automorphism of H. There is a natural epimorphism x - AW & A W — /\W & A W. If X e Av and Y e AW, then o' maps /(X Goc Y) and X& Y into the /*(X (96 y) = A1x &c. Ae y = x3. same value. For we have

**Note**that 9 is ...Page 13

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### Contents

ii | |

vi | |

Application to bundles | 11 |

Thom classes of line bundles | 18 |

Cobordism and homomorphisms into Ktheory | 25 |

The homomorphism e | 30 |

Cobordism Characteristic Classes 58 | 38 |

A theorem of Dold | 39 |

UManifolds with Framed Boundaries | 69 |

The Ubordism groups nº ſº ſº º ſº tº e º º e º º º º | 70 |

Characteristic numbers from Ktheory | 78 |

The theorem of Stong and Hattori | 82 |

Umanifolds with stably framed boundaries | 91 |

The bordism groups Q V fr | 96 |

The groups nº | 105 |

in a | 108 |

Characteristic classes in cobordism | 48 |

Characteristic classes in Ktheory | 52 |

A cobordism interpretation for K X | 65 |

Bibliography | 111 |

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### Common terms and phrases

abelian According acts Adams algebra assigning associated base point basis bordism bordism classes Chapter characteristic Chern classes Chern numbers classes closed U-manifold cobordism coefficient commutativity compact complex vector space composition consider construction COROLLARY CP(n define definition denote diagram dimension element equivalence exact exists fact fiber finite CW complex finite CW pair follows fr)—manifold function give given Hence holds homomorphism Hopf HP(n identified induced integer isomorphism K-theory line bundle linear manifold map f Moreover MU(k Namely natural Note obtain particular partition polynomial Proof prove represented respectively ring seen sequence Similarly stable tangent bundle stably framed structure SU(n sufficient Suppose theorem Thom Todd genus trivial U-structure unique vector space bundle wºn