The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
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... define natural transformations A : D # ( . ) → KO * ( • ) SU ( • ) → k * ( . ) of cohomology theories . Such transformations have been folk theorems since the work of Atiyah - Hirzebruch [ 6 ] , Dold [ 13 ] , and others . It should be ...
... define natural transformations A : D # ( . ) → KO * ( • ) SU ( • ) → k * ( . ) of cohomology theories . Such transformations have been folk theorems since the work of Atiyah - Hirzebruch [ 6 ] , Dold [ 13 ] , and others . It should be ...
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... DEFINITION . By an SU - structure for V we shall mean a unit vector σε V ; suppose an SU - structure has been fixed for V. Define a real linear map : 1 → 1 - ky as follows : fix X & Ʌy and let Y vary overn - ky so that < , XY ) is a ...
... DEFINITION . By an SU - structure for V we shall mean a unit vector σε V ; suppose an SU - structure has been fixed for V. Define a real linear map : 1 → 1 - ky as follows : fix X & Ʌy and let Y vary overn - ky so that < , XY ) is a ...
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... definition of T. ( 1.2 ) We have 72x ( -1 ) k ( n - k ) x for X ε Ʌ * v . Then Proof . It is sufficient to prove ( 1.2 ) for monomials . monomial , TX is the unique monomial with XA TX = σ . Tx ^ x = ( -1 ) k ( n - k ) σ and Define an ...
... definition of T. ( 1.2 ) We have 72x ( -1 ) k ( n - k ) x for X ε Ʌ * v . Then Proof . It is sufficient to prove ( 1.2 ) for monomials . monomial , TX is the unique monomial with XA TX = σ . Tx ^ x = ( -1 ) k ( n - k ) σ and Define an ...
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... defining Y⚫j = ( Y ) for Y & ɅV . Moreover SU ( n ) acts on AV in a quaternionic linear fashion . If n = 4k , let R ... defined an action of the quaternions H on AV , and AV is a quaternionic vector space . Consider g ɛ SU ( n ) . Then ...
... defining Y⚫j = ( Y ) for Y & ɅV . Moreover SU ( n ) acts on AV in a quaternionic linear fashion . If n = 4k , let R ... defined an action of the quaternions H on AV , and AV is a quaternionic vector space . Consider g ɛ SU ( n ) . Then ...
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... define Rody Let Ʌody = Σ 2k + 1v , ^ Σ1 nev v = and Revv . V If n = 2 mod 4 then SU ( n ) od ет spaces V and ^ v . 2k V ; acts on the quaternionic vector If n = 0 mod 4 then SU ( n ) acts on the real vector spaces Rody and Rev. 2 ...
... define Rody Let Ʌody = Σ 2k + 1v , ^ Σ1 nev v = and Revv . V If n = 2 mod 4 then SU ( n ) od ет spaces V and ^ v . 2k V ; acts on the quaternionic vector If n = 0 mod 4 then SU ( n ) acts on the real vector spaces Rody and Rev. 2 ...
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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