The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
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... ) 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 noted that on the coefficient groups , -2n.
... ) 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 noted that on the coefficient groups , -2n.
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... theorems of Stong [ 23 ] and Hattori [ 15 ] . There is a diagram 0 2n → QU , fr → Ω 2n fr 2n - 1 ↓ which gives rise to a homomorphism Td fr FU Ω 2n - 1 → Q / Z . This turns out to coincide with a well - known homomorphism of Adams ...
... theorems of Stong [ 23 ] and Hattori [ 15 ] . There is a diagram 0 2n → QU , fr → Ω 2n fr 2n - 1 ↓ which gives rise to a homomorphism Td fr FU Ω 2n - 1 → Q / Z . This turns out to coincide with a well - known homomorphism of Adams ...
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... theorem of Dold 8. Characteristic classes in cobordism 9. Characteristic classes in K - theory 10. A cobordism interpretation for K * ( X ) 1 1 5 11 18 • 25 • 30 38 39 48 52 59 11. Mappings into spheres 65 Chapter III . U - Manifolds ...
... theorem of Dold 8. Characteristic classes in cobordism 9. Characteristic classes in K - theory 10. A cobordism interpretation for K * ( X ) 1 1 5 11 18 • 25 • 30 38 39 48 52 59 11. Mappings into spheres 65 Chapter III . U - Manifolds ...
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... THEOREM . Consider the complex inner product space V of dimension n , with given SU - structure . If n = 4k + 2 then AV becomes a right quaternionic vector space by defining Y⚫j = ( Y ) for Y & ɅV . Moreover SU ( n ) acts on AV in a ...
... THEOREM . Consider the complex inner product space V of dimension n , with given SU - structure . If n = 4k + 2 then AV becomes a right quaternionic vector space by defining Y⚫j = ( Y ) for Y & ɅV . Moreover SU ( n ) acts on AV in a ...
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... theorem is then proved . v = y ; similarly 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 ...
... theorem is then proved . v = y ; similarly 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 ...
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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