The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 59
... fact , K * ( X , A ) ~ ( * ( X , A ) ® * Z where Z is a * -ring in a natural way . In a similar fashion , * ( X , A ) determines KO * ( X , A ) . U U Sp There is the homomorphism c : Ω 2n U εΩ ωε 2n U U → k2n = Z ; thus for we consider ...
... fact , K * ( X , A ) ~ ( * ( X , A ) ® * Z where Z is a * -ring in a natural way . In a similar fashion , * ( X , A ) determines KO * ( X , A ) . U U Sp There is the homomorphism c : Ω 2n U εΩ ωε 2n U U → k2n = Z ; thus for we consider ...
Page 97
... fact interpret T of compact ( U , fr ) -manifolds . Ω U , fr n n + 2k ( MU ( k ) / s2k ) as bordism classes Thus we define = π ( MU ( k ) / s2k ) , 2k ? n + 2 . n + 2k The method of Thom shows that every element of U , fr is represented ...
... fact interpret T of compact ( U , fr ) -manifolds . Ω U , fr n n + 2k ( MU ( k ) / s2k ) as bordism classes Thus we define = π ( MU ( k ) / s2k ) , 2k ? n + 2 . n + 2k The method of Thom shows that every element of U , fr is represented ...
Page 108
... fact the present exact sequence involving is the same as [ 12 , ( 15.1 ) ] . SU in Ω * 18. The image of ~ w The purpose of this section is the construction of SU 8k + 1 those elements in Ω which can be represented by a stably framed ...
... fact the present exact sequence involving is the same as [ 12 , ( 15.1 ) ] . SU in Ω * 18. The image of ~ w The purpose of this section is the construction of SU 8k + 1 those elements in Ω which can be represented by a stably framed ...
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