The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 28
... KSP ( MSU ( 4k + 2 ) ) as defined in section 3 . KSp ( MSU $ 4k + 2 = s ( follows from section 3 that the map has ዎ ... ( X ) . Let α ε Ãa ̧ ( X ) be repre- : ( X ) → KO1 ( X ) . ∞ & SU → ^ X MSU ( 4k ) . Х SU Let μ ( X ) be the image ...
... KSP ( MSU ( 4k + 2 ) ) as defined in section 3 . KSp ( MSU $ 4k + 2 = s ( follows from section 3 that the map has ዎ ... ( X ) . Let α ε Ãa ̧ ( X ) be repre- : ( X ) → KO1 ( X ) . ∞ & SU → ^ X MSU ( 4k ) . Х SU Let μ ( X ) be the image ...
Page 29
... KSp ( s8k ^ X ) = KSp ( X ) . ( 5.2 ) For each finite CW complex X with base point , commutativity holds in 4 4 Ku2 ( X ) = KO ( s * ^ X ) 4 ñ 2 ( x ) Ms ~ 18 SU where 、 n ) = Proof . KSp ( X ) ( 1-1 ) with the Hopf Sp ( 1 ) -bundle ...
... KSp ( s8k ^ X ) = KSp ( X ) . ( 5.2 ) For each finite CW complex X with base point , commutativity holds in 4 4 Ku2 ( X ) = KO ( s * ^ X ) 4 ñ 2 ( x ) Ms ~ 18 SU where 、 n ) = Proof . KSp ( X ) ( 1-1 ) with the Hopf Sp ( 1 ) -bundle ...
Page 53
... KSP ( X ) = KSP ( X ) . KSp ̊ ( X ) . There is the product KSp ( X ) * KSP ( X ) → KO ( x ) H } mapping ( , 7 ) into the tensor product as in section 3 . By neglecting symplectic structure we can ... ( x ) . ко Namely , Ko1 ( X ) = Ko ( s4 53.
... KSP ( X ) = KSP ( X ) . KSp ̊ ( X ) . There is the product KSp ( X ) * KSP ( X ) → KO ( x ) H } mapping ( , 7 ) into the tensor product as in section 3 . By neglecting symplectic structure we can ... ( x ) . ко Namely , Ko1 ( X ) = Ko ( s4 53.
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