The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 26
... homotopy classes of base point preserving Given f : X → M , there is the ... class of bundle maps 1 + 7 is an SU ( n + 1 ) -bundle , there is a そ n Zn + ... class of bundle maps n k homotopy class of maps MSU ( k ) ^ MSU ( X ) ...
... homotopy classes of base point preserving Given f : X → M , there is the ... class of bundle maps 1 + 7 is an SU ( n + 1 ) -bundle , there is a そ n Zn + ... class of bundle maps n k homotopy class of maps MSU ( k ) ^ MSU ( X ) ...
Page 31
... homotopy class of bundle maps f : E ( 5 ) → Eu ( n ) ' inducing a unique homotopy class of maps f : M ( 5 ) → MU ( n ) . Define - 2n v ( 5 ) ɛ H ̃ ̈ ( M ( 5 ) ) by v ( 5 ) = Î * ( v 。) . f E ( z ) → E ( g ) is a bundle It is easily ...
... homotopy class of bundle maps f : E ( 5 ) → Eu ( n ) ' inducing a unique homotopy class of maps f : M ( 5 ) → MU ( n ) . Define - 2n v ( 5 ) ɛ H ̃ ̈ ( M ( 5 ) ) by v ( 5 ) = Î * ( v 。) . f E ( z ) → E ( g ) is a bundle It is easily ...
Page 105
... course . Note that the cross - section of Bn induces a principal U ( 1 ) -bundle over Bn , which along Bn already has a homotopy class of cross - sections ; thus , the first Chern class c1 ( B ) lies in H * ( вn , aв1 ; Z ) . The ...
... course . Note that the cross - section of Bn induces a principal U ( 1 ) -bundle over Bn , which along Bn already has a homotopy class of cross - sections ; thus , the first Chern class c1 ( B ) lies in H * ( вn , aв1 ; Z ) . The ...
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