The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 30
Pierre E. Conner, E. E. Floyd. 6 . The homomorphism Mc After discussing the cohomology of MU ( n ) and the classical Thom isomorphism theorem , we go on to associate with ** each element of Hˆˆ ( BU ) a homomorphism N * ( x ) → H * ( X ) ...
Pierre E. Conner, E. E. Floyd. 6 . The homomorphism Mc After discussing the cohomology of MU ( n ) and the classical Thom isomorphism theorem , we go on to associate with ** each element of Hˆˆ ( BU ) a homomorphism N * ( x ) → H * ( X ) ...
Page 77
... homomorphism K ( X ) ev → Heˇ ( X ; Q ) [ [ t ] ] assigning to each x & K ( X ) an element T and extending the function 3 → T on bundles . ξ X In particular there is such a homomorphism ( X / A ) → ev ( X / A ; Q ) [ [ t ] ] . ev ...
... homomorphism K ( X ) ev → Heˇ ( X ; Q ) [ [ t ] ] assigning to each x & K ( X ) an element T and extending the function 3 → T on bundles . ξ X In particular there is such a homomorphism ( X / A ) → ev ( X / A ; Q ) [ [ t ] ] . ev ...
Page 104
... homomorphism E : Ω fr → Q / 2 SU 8k + 3 Hence we which coincides with the homomorphism e of Adams [ 3 ] . Let R E SU = E U on Ω fr 8k - 1 ° ( 16.5 ) The homomorphism Esu : integral multiples of 104.
... homomorphism E : Ω fr → Q / 2 SU 8k + 3 Hence we which coincides with the homomorphism e of Adams [ 3 ] . Let R E SU = E U on Ω fr 8k - 1 ° ( 16.5 ) The homomorphism Esu : integral multiples of 104.
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