The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 70
... note its tangent bundle . We shall call the Whitney sum + ( 2k - n ) of and the trivial ( 2k n ) -bundle the stable tangent bundle of м2 , where 2k - n2 2. Note that + ( 2k - - n ) is a real 2k - bundle with space E ( T + ( 2k - n ) ...
... note its tangent bundle . We shall call the Whitney sum + ( 2k - n ) of and the trivial ( 2k n ) -bundle the stable tangent bundle of м2 , where 2k - n2 2. Note that + ( 2k - - n ) is a real 2k - bundle with space E ( T + ( 2k - n ) ...
Page 85
... Note that Adding this to the previous ( xy ) = x y fact that x [ M ] = 0 unless w = 0 or w = ( xy • • • w ) [ M ] = ( p * , ... , pk ) p ) we get ( xy ••• w ) [ M ] mod p ** = x y [ M ] mod p for symmetric x , y , ... , w ɛ K ( M ) ...
... Note that Adding this to the previous ( xy ) = x y fact that x [ M ] = 0 unless w = 0 or w = ( xy • • • w ) [ M ] = ( p * , ... , pk ) p ) we get ( xy ••• w ) [ M ] mod p ** = x y [ M ] mod p for symmetric x , y , ... , w ɛ K ( M ) ...
Page 105
... notes a complete proof of the assertions that ec : Ofr 8k + 5 fr Q / Z is trivial and that the image of ec : Q Ω → Q / Z ... Note that the cross - section of Bn induces a principal U ( 1 ) -bundle over Bn , which along Bn already has a ...
... notes a complete proof of the assertions that ec : Ofr 8k + 5 fr Q / Z is trivial and that the image of ec : Q Ω → Q / Z ... Note that the cross - section of Bn induces a principal U ( 1 ) -bundle over Bn , which along Bn already has a ...
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