The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 16
... finite CW pair we also assume a natural K ( X , A ) similarly for KO and KSp . K ( X / A , x ) ≈ K ( X / A ) ; We return now to the main business of this section . DEFINITION . Let be an SU ( n ) -bundle over a finite CW complex X ...
... finite CW pair we also assume a natural K ( X , A ) similarly for KO and KSp . K ( X / A , x ) ≈ K ( X / A ) ; We return now to the main business of this section . DEFINITION . Let be an SU ( n ) -bundle over a finite CW complex X ...
Page 39
... complex bundles . Fix once and for all a multiplicative cohomology theory ( • ) as in section 4 , defined on the category of finite CW complexes with base point . As is well - known , there is generated a multiplicative cohomology ...
... complex bundles . Fix once and for all a multiplicative cohomology theory ( • ) as in section 4 , defined on the category of finite CW complexes with base point . As is well - known , there is generated a multiplicative cohomology ...
Page 40
... finite CW complex and let yn denote its n - skeleton . Define a filtration F ° n ( x ) > F1n ( x ) > F1h ( X ) Ɔ ••• ƆF2h ( X ) Ɔ ••• r of h ( x ) by Fh ( X ) = Kernel [ 1 * : h ( x ) → h ( x2 - 1 ) ] . Then if a ɛ F3h ( X ) and b ɛ ...
... finite CW complex and let yn denote its n - skeleton . Define a filtration F ° n ( x ) > F1n ( x ) > F1h ( X ) Ɔ ••• ƆF2h ( X ) Ɔ ••• r of h ( x ) by Fh ( X ) = Kernel [ 1 * : h ( x ) → h ( x2 - 1 ) ] . Then if a ɛ F3h ( X ) and b ɛ ...
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