The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 66
... Suppose [ Mon ] has odd Todd genus has [ 8 ] [ w ] = 0. Then [ w ] is a torsion U * has only torsion in its kernel and is a polynomial algebra . Hence we may suppose [ w 66.
... Suppose [ Mon ] has odd Todd genus has [ 8 ] [ w ] = 0. Then [ w ] is a torsion U * has only torsion in its kernel and is a polynomial algebra . Hence we may suppose [ w 66.
Page 67
... Suppose that X is a finite CW complex with * 8n ( X ) a free - module . If f : X → son then f * Ω ŏ * : ( son ) → SU 8n SU Õ * ( X ) is non - trivial if and only if SU f ' : Ko ( son ) → KO ( X ) is non - trivial . Proof . Consider ...
... Suppose that X is a finite CW complex with * 8n ( X ) a free - module . If f : X → son then f * Ω ŏ * : ( son ) → SU 8n SU Õ * ( X ) is non - trivial if and only if SU f ' : Ko ( son ) → KO ( X ) is non - trivial . Proof . Consider ...
Page 87
... Suppose that 9 : Ωυ 2n Z is a homomorphism . Then can be expressed as an integral linear combination of the homomorphisms Sil , ... , 1k 14:00 → → Z , 11 + * • • + 1x ≤ n . - 2n { 11 = 12 2 ... ≥ 1 } , let and n ( w ) = k . Suppose ...
... Suppose that 9 : Ωυ 2n Z is a homomorphism . Then can be expressed as an integral linear combination of the homomorphisms Sil , ... , 1k 14:00 → → Z , 11 + * • • + 1x ≤ n . - 2n { 11 = 12 2 ... ≥ 1 } , let and n ( w ) = k . Suppose ...
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