The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 11
... vector space bundles Rod ( ' ) and Rev ( ' ) over D ( 5 ) , where D ( 5 ) is the bundle 8k space of the bundle ... complex X ; we take to be a right principal SU ( n ) -bundle and denote the bundle space by E ( ) . Fix a complex inner ...
... vector space bundles Rod ( ' ) and Rev ( ' ) over D ( 5 ) , where D ( 5 ) is the bundle 8k space of the bundle ... complex X ; we take to be a right principal SU ( n ) -bundle and denote the bundle space by E ( ) . Fix a complex inner ...
Page 71
... complex vector space bundle . - This complex vector space bundle has Chern classes , which are denoted by k © ( M2 ) € ε н2K ( M2 ) , k = 0,1,2 , n ) receives a natural orientation as a complex Moreover + ( 2k bundle . - Now if we take ...
... complex vector space bundle . - This complex vector space bundle has Chern classes , which are denoted by k © ( M2 ) € ε н2K ( M2 ) , k = 0,1,2 , n ) receives a natural orientation as a complex Moreover + ( 2k bundle . - Now if we take ...
Page 93
... complex vector space bundle on M with a given trivialization , as a complex vector space bundle , when restricted to aм " . - Denote by the stable tangent bundle of м " , a bundle of k - dimensional complex vector spaces . Moreover we ...
... complex vector space bundle on M with a given trivialization , as a complex vector space bundle , when restricted to aм " . - Denote by the stable tangent bundle of м " , a bundle of k - dimensional complex vector spaces . Moreover we ...
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