The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 4
... Consider the complex inner product space V of dimension n , with given SU - structure & Av . If n = 4k + 2 then AV ☛ becomes a right quaternionic vector space by defining Y.j = μ ( Y ) for Y & AV . Moreover SU ( n ) acts on AV in a ...
... Consider the complex inner product space V of dimension n , with given SU - structure & Av . If n = 4k + 2 then AV ☛ becomes a right quaternionic vector space by defining Y.j = μ ( Y ) for Y & AV . Moreover SU ( n ) acts on AV in a ...
Page 12
... 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 , where R ( 3 ) = { › x : x ε 1 ( 5 ) , μx = x ) ...
... 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 , where R ( 3 ) = { › x : x ε 1 ( 5 ) , μx = x ) ...
Page 55
... consider μ : * ( · ) position → KO * ( • ) , the com- Sp * ( * ~ ( • ) → ( * Sp SU ( • ) μ KO * ( • ) ( 9.3 ) THEOREM . Let complex X , and let ( 5 ) & k of ( 8.2 ) and ( 9.2 ) . Then Proof . We have that denote an Sp ( m ) -bundle ...
... consider μ : * ( · ) position → KO * ( • ) , the com- Sp * ( * ~ ( • ) → ( * Sp SU ( • ) μ KO * ( • ) ( 9.3 ) THEOREM . Let complex X , and let ( 5 ) & k of ( 8.2 ) and ( 9.2 ) . Then Proof . We have that denote an Sp ( m ) -bundle ...
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