The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 53
... namely any element with ph✈ the image of a generator under ( sk ; Z ) → Hk ( sk ; Q ) . We also need a little information concerning KSP ( X ) = KSP ( X ) . KSp ̊ ( X ) . There is the product KSp ( X ) * KSP ( X ) → KO ( x ) H ...
... namely any element with ph✈ the image of a generator under ( sk ; Z ) → Hk ( sk ; Q ) . We also need a little information concerning KSP ( X ) = KSP ( X ) . KSp ̊ ( X ) . There is the product KSp ( X ) * KSP ( X ) → KO ( x ) H ...
Page 54
Pierre E. Conner, E. E. Floyd. Namely , Ko1 ( X ) = Ko ( s4 x ) and given 重して( ༩ ) KO = KO KO ( s1 ^ X ) ( 1-5 ) where 1 e KSP ( X ) we let ʼn KSP ( X ) is the Hopf Sp ( 1 ) -bundle over = ch 7 · st . It follows from the above ...
Pierre E. Conner, E. E. Floyd. Namely , Ko1 ( X ) = Ko ( s4 x ) and given 重して( ༩ ) KO = KO KO ( s1 ^ X ) ( 1-5 ) where 1 e KSP ( X ) we let ʼn KSP ( X ) is the Hopf Sp ( 1 ) -bundle over = ch 7 · st . It follows from the above ...
Page 78
... namely in is given as follows : ( 1 -。- t1 , . . . ( 1 e - e 。- tn ) } n replace t1 by c1 ( ) , 13 . Σt1t by ck ( 3 ) , Κ 1 Characteristic numbers from K - theory . 2n Assume that we are given a compact U - manifold M and an element x ...
... namely in is given as follows : ( 1 -。- t1 , . . . ( 1 e - e 。- tn ) } n replace t1 by c1 ( ) , 13 . Σt1t by ck ( 3 ) , Κ 1 Characteristic numbers from K - theory . 2n Assume that we are given a compact U - manifold M and an element x ...
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