The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 18
... bundle over a space X and そ a U ( n ) -bundle over Y. Then we identify M ( = × × ) with M ( 5 ) ^ M ( ) . The product X ( M ( 5 ) ) © Ã ( M ( 7 ) ) → X ( M ( 5 ) ^ M ( ~ ) ) = K ( 1 ... bundle . Form the 18 Thom classes of line bundles 1.
... bundle over a space X and そ a U ( n ) -bundle over Y. Then we identify M ( = × × ) with M ( 5 ) ^ M ( ) . The product X ( M ( 5 ) ) © Ã ( M ( 7 ) ) → X ( M ( 5 ) ^ M ( ~ ) ) = K ( 1 ... bundle . Form the 18 Thom classes of line bundles 1.
Page 20
... line bundle over D ( § ) ; let 1 denote the trivial quaternionic line bundle over E ( ) • Sp ( 1 ) / Sp ( 1 ) . There is the bundle map F : ev ( §1 ) → 1 defined by F ( x , w ) = ( f ( x ) , w ) for x & D ( 5 ) and w ɛ H , where f is ...
... line bundle over D ( § ) ; let 1 denote the trivial quaternionic line bundle over E ( ) • Sp ( 1 ) / Sp ( 1 ) . There is the bundle map F : ev ( §1 ) → 1 defined by F ( x , w ) = ( f ( x ) , w ) for x & D ( 5 ) and w ɛ H , where f is ...
Page 21
... bundle § over HP ( n - 1 ) ; we also n - 1 the associated quaternionic line bundle over HP ( n - 1 ) . denote by We may regard n - 1 4n - 1 S = Sp ( 1 ) • Sp ( 1 ) , HP ( n - 1 ) ... line bundles . In particular , ( 4.4 ) - The Hopf U 21.
... bundle § over HP ( n - 1 ) ; we also n - 1 the associated quaternionic line bundle over HP ( n - 1 ) . denote by We may regard n - 1 4n - 1 S = Sp ( 1 ) • Sp ( 1 ) , HP ( n - 1 ) ... line bundles . In particular , ( 4.4 ) - The Hopf U 21.
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