The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
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... elements of ( U , fr n are interpreted as bordism classes [ M ] of compact ( U , fr ) -manifolds M , where roughly a ( U , fr ) -manifold is a differentiable manifold M with a given complex structure on its stable tangent bundle T and a ...
... elements of ( U , fr n are interpreted as bordism classes [ M ] of compact ( U , fr ) -manifolds M , where roughly a ( U , fr ) -manifold is a differentiable manifold M with a given complex structure on its stable tangent bundle T and a ...
Page 1
... element over a finite CW complex X there is con- ( 3 ) ɛ K ( M ( ) ) where M ( ) is the Thom space of § ; we call J ( 5 ) the Thom class of § . Similarly given an SU ( 4k ) -bundle there is constructed a Thom class t ( 3 ) ɛ KO ( M ( 5 ) ...
... element over a finite CW complex X there is con- ( 3 ) ɛ K ( M ( ) ) where M ( ) is the Thom space of § ; we call J ( 5 ) the Thom class of § . Similarly given an SU ( 4k ) -bundle there is constructed a Thom class t ( 3 ) ɛ KO ( M ( 5 ) ...
Page 2
... ) 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.
... ) 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
... element X = - erl Λ · A erk where г1 < ... < Ik if X and Y are monomials , then 1 if Y X < X , Y > = -1 if Y = -X U otherwise . Moreover given a monomial X there is a unique monomial X with X x = ( 1.1 ) If X is a monomial then X is the ...
... element X = - erl Λ · A erk where г1 < ... < Ik if X and Y are monomials , then 1 if Y X < X , Y > = -1 if Y = -X U otherwise . Moreover given a monomial X there is a unique monomial X with X x = ( 1.1 ) If X is a monomial then X is the ...
Page 7
... element q as + j where α , ßɛ c ε - ; this is an anti - automorphism of H. There is a natural epimorphism AV d ' : ^ V R ^ w → Av R ® C 1W . H If X ε AV and Y ɛ Aw , then ɣ ' maps μ ( X ® Y ) and X Y into the same value . For we have ...
... element q as + j where α , ßɛ c ε - ; this is an anti - automorphism of H. There is a natural epimorphism AV d ' : ^ V R ^ w → Av R ® C 1W . H If X ε AV and Y ɛ Aw , then ɣ ' maps μ ( X ® Y ) and X Y into the same value . For we have ...
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Common terms and phrases
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