The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 66
... represents a non - zero element of SU 8m ε Ω Im / Im . Finally if [ м3n ] e ΕΩ SU 8n has odd Todd genus , then [ мon ] represents a non - zero element of Im SU / Im [ 12 , p . 70 ] . We can now prove our assertion . and that [ w ] N W ε ...
... represents a non - zero element of SU 8m ε Ω Im / Im . Finally if [ м3n ] e ΕΩ SU 8n has odd Todd genus , then [ мon ] represents a non - zero element of Im SU / Im [ 12 , p . 70 ] . We can now prove our assertion . and that [ w ] N W ε ...
Page 67
... represents 0 in Im SU [ wk ] [ v8m ] [ §1 ] [ §1 ] . Then = 8m / Im 0 . Since this is a polynomial algebra , then [ vom ] represents zero in Im Qs / Im and [ w ] = 0. The lemma follows . ã * SU ( 11.2 ) THEOREM . Suppose that X is a ...
... represents 0 in Im SU [ wk ] [ v8m ] [ §1 ] [ §1 ] . Then = 8m / Im 0 . Since this is a polynomial algebra , then [ vom ] represents zero in Im Qs / Im and [ w ] = 0. The lemma follows . ã * SU ( 11.2 ) THEOREM . Suppose that X is a ...
Page 100
... representing fr 2n - 1 Using the natural embedding i : skC MU ( k ) , we get f ' = if : s as representing an element of T 2n + 2k - 1 2n + 2k - 1 exists an extension of f ' to a map → MU ( k ) . Regard f ' ( MU ( k ) ) = = 0 , there 2n ...
... representing fr 2n - 1 Using the natural embedding i : skC MU ( k ) , we get f ' = if : s as representing an element of T 2n + 2k - 1 2n + 2k - 1 exists an extension of f ' to a map → MU ( k ) . Regard f ' ( MU ( k ) ) = = 0 , there 2n ...
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