## The Relation of Cobordism to K-Theories |

### From inside the book

Results 1-5 of 51

Page

and are called cobordism theories; the homology theories are aenoa by do.), no"(...), o:*C.) and are called bordism theories. The coefficient groups are, taking one case as an example,

and are called cobordism theories; the homology theories are aenoa by do.), no"(...), o:*C.) and are called bordism theories. The coefficient groups are, taking one case as an example,

**given**by () =0; (point), o -0. Page

The elements or 0. fr are interpreted as bordism classes LM”) of compact (U, fr)—manifolds M”, where roughly a (U, fr)—manifold is a differentiable manifold M with a

The elements or 0. fr are interpreted as bordism classes LM”) of compact (U, fr)—manifolds M”, where roughly a (U, fr)—manifold is a differentiable manifold M with a

**given**complex structure on its stable tangent bundle to and a**given**... Page

It is proved that

It is proved that

**given**a compact (U, fr)-manifold *, there is a closed weakly almost complex manifold having the same Chern numbers 2n as M if and only if Td [*] is an integer; this makes use of recent theorems of Stong [23] and ... Page i

96 The groups no * ................................. 105 The image of 0:" in a "...................... . . . . 108 CHAPTER I. THE THOM ISOMORPHISM IN K–THEORY.

96 The groups no * ................................. 105 The image of 0:" in a "...................... . . . . 108 CHAPTER I. THE THOM ISOMORPHISM IN K–THEORY.

**Given**a U(n)-bundle. 12. 13. 14. 15. 16. 17. 18. Bibliography • . Page ii

**Given**a U(n)-bundle 5 over a finite CW complex X there is conStructed an element J ( ; ) 8. Kūstā )) where M( ; ) is the Thom space of 5 ; we call J ( 3 ) the Thom class of 5 . Similarly**given**an SU(4k)—bundle there is constructed a ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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 |

### Other editions - View all

### 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