The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 45
... assigning to each Sp ( m ) -bundle over a finite CW complex X ( m arbitrary ) an element p ( } ) = 1 + = 1 + P1 ( ) + 5 Pm ( 5 ) 4k PK where ( 5 ) & h ( x ) , such that ( 1 ) a bundle map f : 3 → covering a map covering a map f : XY of ...
... assigning to each Sp ( m ) -bundle over a finite CW complex X ( m arbitrary ) an element p ( } ) = 1 + = 1 + P1 ( ) + 5 Pm ( 5 ) 4k PK where ( 5 ) & h ( x ) , such that ( 1 ) a bundle map f : 3 → covering a map covering a map f : XY of ...
Page 54
... generator of H1n ( HP ( n ) ) . The proof now goes exactly as ( 8.1 ) . ( 9.2 ) COROLLARY . There exists a unique function assigning to each Sp ( m ) -bundle over a finite CW complex X an element ( ૬ ) 4k = where ( 5 ) ɛ 54.
... generator of H1n ( HP ( n ) ) . The proof now goes exactly as ( 8.1 ) . ( 9.2 ) COROLLARY . There exists a unique function assigning to each Sp ( m ) -bundle over a finite CW complex X an element ( ૬ ) 4k = where ( 5 ) ɛ 54.
Page 77
... 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 Identifying ( X / A ) with K ( X , A ) and He ( X / A ...
... 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 Identifying ( X / A ) with K ( X , A ) and He ( X / 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