The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 24
Pierre E. Conner, E. E. Floyd. According to ( 3.3 ) , complexification KO ( S ) → Ẵ 8 → X ( so ) 8 ) maps Proof . t ... According to the proof of ( 4.5 ) , if is the U ( n ) -bundle over a ~ 2n K point , then J ( 5 ) is a generator of ...
Pierre E. Conner, E. E. Floyd. According to ( 3.3 ) , complexification KO ( S ) → Ẵ 8 → X ( so ) 8 ) maps Proof . t ... According to the proof of ( 4.5 ) , if is the U ( n ) -bundle over a ~ 2n K point , then J ( 5 ) is a generator of ...
Page 55
... s ( 5 ( 7 ) = 1 - } according to ( 4.2 ) . N + 1 Now p1 is represented by i : HP ( n ) CHP ( N + 1 ) , hence n ड / s ( P'n ) = 1 ' ( s ( 7 ) ) = 1 - 32 ' 1` ( s ( ? ) ) The theorem then follows . It is convenient to extract 55.
... s ( 5 ( 7 ) = 1 - } according to ( 4.2 ) . N + 1 Now p1 is represented by i : HP ( n ) CHP ( N + 1 ) , hence n ड / s ( P'n ) = 1 ' ( s ( 7 ) ) = 1 - 32 ' 1` ( s ( ? ) ) The theorem then follows . It is convenient to extract 55.
Page 66
... According to section 5 , -8n ( - ) U ε SU N * ( • ) U K2 KO * ( • ) + Kc → K ^ ( . ) -3n has μcß'8n ' U = ± 1 . Using the U isomorphism≈ - 8n , the element [ on ] & corresponding to commutes , hence U + has Todd genus T [ M ] = 1 8n ...
... According to section 5 , -8n ( - ) U ε SU N * ( • ) U K2 KO * ( • ) + Kc → K ^ ( . ) -3n has μcß'8n ' U = ± 1 . Using the U isomorphism≈ - 8n , the element [ on ] & corresponding to commutes , hence U + has Todd genus T [ M ] = 1 8n ...
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