The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 11
... constructions of the preceding sections are applied to U ( n ) -bundles and SU ( n ) -bundles . For example , given ... construction , one obtains an element t ( ) ɛ KO ( D ( 5 ) , D ( 5 ) ) where t ( ) d ( ^ ev ( §1 ) , 1od ( 5 ' ) , Q ) ...
... constructions of the preceding sections are applied to U ( n ) -bundles and SU ( n ) -bundles . For example , given ... construction , one obtains an element t ( ) ɛ KO ( D ( 5 ) , D ( 5 ) ) where t ( ) d ( ^ ev ( §1 ) , 1od ( 5 ' ) , Q ) ...
Page 37
... construction one simply puts a suitable complex structure on the stable tangent bundle of 2n . ( 6.5 ) COROLLARY . The composition Mc K ( pt ) = Z -2n Ωυ ≈ Ω ( pt ) 2n U maps a cobordism class [ M2n ] of closed weakly complex manifolds ...
... construction one simply puts a suitable complex structure on the stable tangent bundle of 2n . ( 6.5 ) COROLLARY . The composition Mc K ( pt ) = Z -2n Ωυ ≈ Ω ( pt ) 2n U maps a cobordism class [ M2n ] of closed weakly complex manifolds ...
Page 108
... construction of SU 8k + 1 those elements in Ω which can be represented by a stably framed closed manifold . fr ( 18.1 ) LEMMA : Let [ v ] ɛ ( εΩ n [ MK ] εΩ SU be an element whose image in fr n + k be an element of order 2 and let SU ...
... construction of SU 8k + 1 those elements in Ω which can be represented by a stably framed closed manifold . fr ( 18.1 ) LEMMA : Let [ v ] ɛ ( εΩ n [ MK ] εΩ SU be an element whose image in fr n + k be an element of order 2 and let SU ...
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