## The Relation of Cobordism to K-Theories |

### From inside the book

Results 1-5 of 46

Page

The

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 ii

Given a U(n)-bundle 5 over a finite CW complex X there is conStructed an

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 ... Page iii

... suppose an SU-structure has been fixed for W. Define a real linear map C': A*w -> An-ky as follows: fix X e A*w and let Y vary over A **w so that 3-,x a Y > is a linear map An-ky — C; define ^ X to be the unique

... suppose an SU-structure has been fixed for W. Define a real linear map C': A*w -> An-ky as follows: fix X e A*w and let Y vary over A **w so that 3-,x a Y > is a linear map An-ky — C; define ^ X to be the unique

**element**of A*w such ... Page iv

By a monomial of AW we mean an

By a monomial of AW we mean an

**element**x = er, A • * > /* °rk where r1 4- - - - K. rk. It is seen that if X and Y are monomials, then l if Y < X,Y > = —l if Y X -X 0 otherwise. ,” of * Moreover given a monomial X there is a unique ... Page viii

Define a left action of H on AW by q-Y = Y-q, so that we obtain a real vector space A V (3) A W. Here we write an

Define a left action of H on AW by q-Y = Y-q, so that we obtain a real vector space A V (3) A W. Here we write an

**element**q as ex + A3 where of , /*e C and aerine q = 2^ –73 j; this is an anti-automorphism of H. There is a natural ...### 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