The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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... Characteristic classes in cobordism 9. Characteristic classes in K - theory 10. A cobordism interpretation for K * ( X ) 11. Mappings into spheres 38 39 48 52 59 65 Chapter III . U - Manifolds with Framed Boundaries 69 U 12. The U ...
... Characteristic classes in cobordism 9. Characteristic classes in K - theory 10. A cobordism interpretation for K * ( X ) 11. Mappings into spheres 38 39 48 52 59 65 Chapter III . U - Manifolds with Framed Boundaries 69 U 12. The U ...
Page 48
... Characteristic classes in cobordism . In this section we set up central tools for this chapter . Recall that in ... characteristic classes p ( 5 ) e ( 4k ( X ) ; it will sometimes be convenient to use k Sp Ω ( • ) → ( ) * ( • ) ̊ to ...
... Characteristic classes in cobordism . In this section we set up central tools for this chapter . Recall that in ... characteristic classes p ( 5 ) e ( 4k ( X ) ; it will sometimes be convenient to use k Sp Ω ( • ) → ( ) * ( • ) ̊ to ...
Page 52
... Characteristic classes in K - theory . There was defined in section 5 a homomorphism ( . ) → KO * ( . ) ; we also denote the composition Ω ( 2 p ( · ) → * u ( · ) > xo * ( - ) Q * Sp ( • ) →→→ KO * ( • ) . by Mi ( * ( • ) Sp CW ...
... Characteristic classes in K - theory . There was defined in section 5 a homomorphism ( . ) → KO * ( . ) ; we also denote the composition Ω ( 2 p ( · ) → * u ( · ) > xo * ( - ) Q * Sp ( • ) →→→ KO * ( • ) . by Mi ( * ( • ) Sp CW ...
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