The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 15
... exact sequence of bundles U → 50 О → n 1x Po < → 0 . It may be verified that for n large there exists a linear monomorphism ड 1 맞 extending the composition | A 31 & 5 | A There is A then an exact sequence 0 → 51 → n P1 → 0 ...
... exact sequence of bundles U → 50 О → n 1x Po < → 0 . It may be verified that for n large there exists a linear monomorphism ड 1 맞 extending the composition | A 31 & 5 | A There is A then an exact sequence 0 → 51 → n P1 → 0 ...
Page 44
... exact Mayer- Vietoris triangle h ( X'X ' ' ) → h ( X ' ) + h ( x ' ' ) T h ( X ' ( ) X ' ' ) . Since M is free , we also have the exact triangle h ( X ' ~ X ' ' ) ( h M → h ( X ' ) X M + h ( X ' ' ) h h ( X ' ( ) ) X ' ' ) @ M. There ...
... exact Mayer- Vietoris triangle h ( X'X ' ' ) → h ( X ' ) + h ( x ' ' ) T h ( X ' ( ) X ' ' ) . Since M is free , we also have the exact triangle h ( X ' ~ X ' ' ) ( h M → h ( X ' ) X M + h ( X ' ' ) h h ( X ' ( ) ) X ' ' ) @ M. There ...
Page 59
... all except exactness . eventually turn out that A ^ ( . ) is also exact . * There is the natural epimorphism ß : * It will Q ( X , A ) → Ả ( X , A ) U defined by B ( c ) = c1 . There 59 A cobordism interpretation for K*
... all except exactness . eventually turn out that A ^ ( . ) is also exact . * There is the natural epimorphism ß : * It will Q ( X , A ) → Ả ( X , A ) U defined by B ( c ) = c1 . There 59 A cobordism interpretation for K*
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