The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 48
... classes in cobordism . In this section we set up central tools for this chapter . Recall that in section 5 we have ... classes p ( 5 ) e ( 4k ( X ) ; it will sometimes be convenient to use k Sp Ω ( • ) → ( ) * ( • ) ̊ to consider ...
... classes in cobordism . In this section we set up central tools for this chapter . Recall that in section 5 we have ... classes p ( 5 ) e ( 4k ( X ) ; it will sometimes be convenient to use k Sp Ω ( • ) → ( ) * ( • ) ̊ to consider ...
Page 69
... class . In particular there are the integers S s ε [ M ] where the £ K ( M ) are certain K - theory characteristic classes of the stable tangent bundle . In section 14 we give the proof of Stong [ 23 ] that every homomorphism s Ωυ → Z ...
... class . In particular there are the integers S s ε [ M ] where the £ K ( M ) are certain K - theory characteristic classes of the stable tangent bundle . In section 14 we give the proof of Stong [ 23 ] that every homomorphism s Ωυ → Z ...
Page 75
... classes , there is the formula ω ) = S ( 3 ) .s Wit wil ω ( 7 ) Sw ( 5 + = Σ If мn is a U - manifold we may consider the stable tangent bundle - k ̃1 ( M3 ) ɛ K ( M3 ) ; similarly there are the classes ( m3 ) ɛ K ( M2 ) . The total class ...
... classes , there is the formula ω ) = S ( 3 ) .s Wit wil ω ( 7 ) Sw ( 5 + = Σ If мn is a U - manifold we may consider the stable tangent bundle - k ̃1 ( M3 ) ɛ K ( M3 ) ; similarly there are the classes ( m3 ) ɛ K ( M2 ) . The total class ...
Contents
The Thom Isomorphism in Ktheory | 1 |
Cobordism Characteristic Classes | 38 |
UManifolds with Framed Boundaries | 69 |
Copyright | |
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abelian group algebra base point bordism bordism classes bordism groups bundle map ch+k characteristic classes Chern classes Chern numbers closed U-manifold cobordism cohomology theory complex inner product complex vector space composition consider COROLLARY CP(n CW pair X,A define denote diagram dimension Dold epimorphism fiber finite CW complex finite CW pair fr)-manifold framed manifold Hence homotopy class Hopf HP(n identified induced inner product space integer K-theory kernel KSP(X LEMMA line bundle linear M²n map f Milnor monomial MSU 4k MU(k multiplicative cohomology theory n)-bundle ñ¹ ñ¹(x P₁ partition polynomial Proof quaternionic quaternionic vector space Similarly stable tangent bundle stably framed manifold SU(n Suppose theorem Thom class Thom space Todd genus trivial U-structure U(n)-bundle vector space bundle Z-graded εΩ Ωυ