The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 12
... respectively in the above , we obtain bundles od Λ 1 ( 5 ) → X and ev ^ ( 5 ) → X. If n = 2 mod 4 then μ defines a quaternionic bundle structure on A ( ) , so that in this case we consider ( 5 ) → X a quaternionic vector space bundle ...
... respectively in the above , we obtain bundles od Λ 1 ( 5 ) → X and ev ^ ( 5 ) → X. If n = 2 mod 4 then μ defines a quaternionic bundle structure on A ( ) , so that in this case we consider ( 5 ) → X a quaternionic vector space bundle ...
Page 48
... respectively then c ( 5 C N ) =そ C ( 3 ) • C ( 7 ) , ( 3 ) if is the Hopf U ( 1 ) -bundle over CP ( n ) , then = c ( Sn ) = 1 + 2 n ° n Naturally the proof is just as above , based on the fibering π : CP ( 3 ) → X with fiber CP ( n 8 ...
... respectively then c ( 5 C N ) =そ C ( 3 ) • C ( 7 ) , ( 3 ) if is the Hopf U ( 1 ) -bundle over CP ( n ) , then = c ( Sn ) = 1 + 2 n ° n Naturally the proof is just as above , based on the fibering π : CP ( 3 ) → X with fiber CP ( n 8 ...
Page 105
... respectively denote the associated bundle with fibre 0 ( 2m ) / U ( m ) and 0 ( 2m ) / SU ( m ) . There is the principal fibring SU U with fibre U ( m ) / SU ( m ) n n = U ( 1 ) . A ( U , SU ) -structure on Bn is a pair consisting of a ...
... respectively denote the associated bundle with fibre 0 ( 2m ) / U ( m ) and 0 ( 2m ) / SU ( m ) . There is the principal fibring SU U with fibre U ( m ) / SU ( m ) n n = U ( 1 ) . A ( U , SU ) -structure on Bn is a pair consisting of a ...
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