The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 69
... classes [ M ] of closed differentiable manifolds with a given complex structure on the stable tangent bundle . In ... Chern classes and Chern numbers , hence also a Todd genus Td [ M ] which is now a rational 2n M number . It is proved ...
... classes [ M ] of closed differentiable manifolds with a given complex structure on the stable tangent bundle . In ... Chern classes and Chern numbers , hence also a Todd genus Td [ M ] which is now a rational 2n M number . It is proved ...
Page 71
... Chern classes , which are denoted by k © ( M2 ) € ε н2K ( M2 ) , k = 0,1,2 , n ) receives a natural orientation as a complex Moreover + ( 2k bundle . - Now if we take two different representatives of it is not hard to see that we obtain ...
... Chern classes , which are denoted by k © ( M2 ) € ε н2K ( M2 ) , k = 0,1,2 , n ) receives a natural orientation as a complex Moreover + ( 2k bundle . - Now if we take two different representatives of it is not hard to see that we obtain ...
Page 74
... Chern numbers . This number is also 2n denoted by $ 11 ' [ M2n ] . According ... classes ( see [ 5 ] ) ; their existence follows easily from ( 7.6 ) . r k ... Chern classes k of Chapter II . Just as for cohomology Chern classes , we can ...
... Chern numbers . This number is also 2n denoted by $ 11 ' [ M2n ] . According ... classes ( see [ 5 ] ) ; their existence follows easily from ( 7.6 ) . r k ... Chern classes k of Chapter II . Just as for cohomology Chern classes , we can ...
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