The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 11
... vector space bundles Rod ( ' ) and Rev ( ' ) over D ( 5 ) , where D ( 5 ) is the bundle 8k space of the bundle associated with with fiber the unit ball D. There is also a linear isomorphism od 9 : R ev ( 5 ' ) | JD ( 3 ) ≈ R ...
... vector space bundles Rod ( ' ) and Rev ( ' ) over D ( 5 ) , where D ( 5 ) is the bundle 8k space of the bundle associated with with fiber the unit ball D. There is also a linear isomorphism od 9 : R ev ( 5 ' ) | JD ( 3 ) ≈ R ...
Page 12
... bundle structure on A ( ) , so that in this case we consider ( 5 ) → X a quaternionic vector space bundle . Clearly ( ) splits as the Whitney sum 1 ev ( 5 ) 100 ( 5 ) . If n = 0 mod 4 , we get a real vector space bundle R ( ) → X ...
... bundle structure on A ( ) , so that in this case we consider ( 5 ) → X a quaternionic vector space bundle . Clearly ( ) splits as the Whitney sum 1 ev ( 5 ) 100 ( 5 ) . If n = 0 mod 4 , we get a real vector space bundle R ( ) → X ...
Page 13
... vector space bundles while in cases 2 and 3 they are equivalent as quaternionic vector space bundles . 9 V We next give the significance of the maps of section 2. Let be an SU ( n ) -bundle over the finite CW complex X. Let 2n E ( 5 ) ...
... vector space bundles while in cases 2 and 3 they are equivalent as quaternionic vector space bundles . 9 V We next give the significance of the maps of section 2. Let be an SU ( n ) -bundle over the finite CW complex X. Let 2n E ( 5 ) ...
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