The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 14
... define the groups K ( X , A ) , KO ( X , A ) , KSp ( X , A ) , using a definition that builds in Atiyah's difference construction [ 7,22 ] . Fix a pair ( X , A ) of finite CW complexes ; also fix one of the classes of complex , real or ...
... define the groups K ( X , A ) , KO ( X , A ) , KSp ( X , A ) , using a definition that builds in Atiyah's difference construction [ 7,22 ] . Fix a pair ( X , A ) of finite CW complexes ; also fix one of the classes of complex , real or ...
Page 16
... DEFINITION . Let be an SU ( n ) -bundle over a finite CW complex X. Define the Thom space M ( ) to be D ( § ) / JD ( § ) . If n = 4k + 2 , con- sider the triple ( ev ( ' ) , od ( 51 ) , f ) of ( 3.2 ) , where the bundles are ...
... DEFINITION . Let be an SU ( n ) -bundle over a finite CW complex X. Define the Thom space M ( ) to be D ( § ) / JD ( § ) . If n = 4k + 2 , con- sider the triple ( ev ( ' ) , od ( 51 ) , f ) of ( 3.2 ) , where the bundles are ...
Page 20
... defined by F ( x , w ) = ( f ( x ) , w ) for x & D ( 5 ) and w ɛ H , where f is defined in the proof of ( 4.1 ) . We next obtain a bundle map G : G ' : ( E ( 5 ) × D3 ) × H → 1od ( 51 ) → . →そ( E ( ▽ ) • Sp ( 1 ) ) × H There is ...
... defined by F ( x , w ) = ( f ( x ) , w ) for x & D ( 5 ) and w ɛ H , where f is defined in the proof of ( 4.1 ) . We next obtain a bundle map G : G ' : ( E ( 5 ) × D3 ) × H → 1od ( 51 ) → . →そ( E ( ▽ ) • Sp ( 1 ) ) × H There is ...
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