The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 5
... obtain a Z - graded real vector space RV . A main purpose of this section is to prove the following . There exist natural isomorphisms ( 2.1 ) THEOREM . R ( VW ) ~ R ( V ) R ( W ) , m = 4k , n = 4X R ^ ( V + W ) ~ R ( V ) , A ( W ) ...
... obtain a Z - graded real vector space RV . A main purpose of this section is to prove the following . There exist natural isomorphisms ( 2.1 ) THEOREM . R ( VW ) ~ R ( V ) R ( W ) , m = 4k , n = 4X R ^ ( V + W ) ~ R ( V ) , A ( W ) ...
Page 12
... obtain bundles od Λ 1 ( 5 ) → X and ev ^ ( 5 ) → X. If n = 2 mod 4 then μ defines a quaternionic bundle structure on A ( ) , so that in this case we consider ( 5 ) → X a quaternionic vector space bundle . Clearly ( ) splits as the ...
... obtain bundles od Λ 1 ( 5 ) → X and ev ^ ( 5 ) → X. If n = 2 mod 4 then μ defines a quaternionic bundle structure on A ( ) , so that in this case we consider ( 5 ) → X a quaternionic vector space bundle . Clearly ( ) splits as the ...
Page 49
... obtain a universal Sp ( 1 ) -bundle over HP ( ∞ ) , and = MSp ( 1 ) M ( 5 ) ≈ HP ( ∞ ) . For each n , the inclusion i : HP ( n ) C HP ( ) represents an element of [ HP ( n ) , MSp ( 1 ) ] . By suspension we obtain an element 4k Pn Pn ...
... obtain a universal Sp ( 1 ) -bundle over HP ( ∞ ) , and = MSp ( 1 ) M ( 5 ) ≈ HP ( ∞ ) . For each n , the inclusion i : HP ( n ) C HP ( ) represents an element of [ HP ( n ) , MSp ( 1 ) ] . By suspension we obtain an element 4k Pn Pn ...
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