The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
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Page 2
... XY ) is a linear map TX to be the unique element of n - ky such that n - ky VC ; define < ~ X , Y ) = ( 0 , x ^ Y > , all Y ɛ ^ n - kv . Ʌn - ky . It is then seen that the above equation holds for 20 Tensor products of exterior algebras.
... XY ) is a linear map TX to be the unique element of n - ky such that n - ky VC ; define < ~ X , Y ) = ( 0 , x ^ Y > , all Y ɛ ^ n - kv . Ʌn - ky . It is then seen that the above equation holds for 20 Tensor products of exterior algebras.
Page 3
... unique monomial X with X x = ( 1.1 ) If X is a monomial then X is the unique monomial X with X ^ x = 0 . This is readily seen from the definition of T. ( 1.2 ) We have 72x ( -1 ) k ( n - k ) x for X ε Ʌ * v . Then Proof . It is ...
... unique monomial X with X x = ( 1.1 ) If X is a monomial then X is the unique monomial X with X ^ x = 0 . This is readily seen from the definition of T. ( 1.2 ) We have 72x ( -1 ) k ( n - k ) x for X ε Ʌ * v . Then Proof . It is ...
Page 6
... unique monomial X with X ^ X = 1 = σ 2 ° the unique monomial Y with Y A Y = σ Then ( X ^ X ) ® ( Y ^ Y ) = σ- ( −1 ) s ( m - r ) ( x® Y ) ^ ( X® I ) = σ and T ( XY ) = ( −1 ) S ( m - r ) T12Y . Since ∞ ( X © Y ) = ( -1 ) rs xx® xy ...
... unique monomial X with X ^ X = 1 = σ 2 ° the unique monomial Y with Y A Y = σ Then ( X ^ X ) ® ( Y ^ Y ) = σ- ( −1 ) s ( m - r ) ( x® Y ) ^ ( X® I ) = σ and T ( XY ) = ( −1 ) S ( m - r ) T12Y . Since ∞ ( X © Y ) = ( -1 ) rs xx® xy ...
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abelian group algebra base point bordism bordism classes BSp(n bundle map c₁ ch+k characteristic classes Chern classes Chern numbers closed U-manifold cobordism coefficient groups cohomology theory complex inner product complex vector space consider COROLLARY CP(n CW pair X,A define denote diagram dimension Dold element epimorphism ɛ K(M finite CW complex finite CW pair framed manifold Hence Hirzebruch homotopy class Hopf HP(n identified induced inner product space integer K-theory kernel KSP(X LEMMA line bundle M²n map f module monomial MSU 4k MU(k multiplicative cohomology theory n+2k 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 unitary vector space bundle Z-graded εΩ Ωυ हु