The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 1
Pierre E. Conner, E. E. Floyd. CHAPTER I. THE THOM ISOMORPHISM IN K - THEORY . Given a U ( n ) -bundle over a finite CW complex X there is con- structed an element J ( ) & K ( M ( ) ) where M ( 5 ) ... Isomorphism in K-theory Exterior Algebra.
Pierre E. Conner, E. E. Floyd. CHAPTER I. THE THOM ISOMORPHISM IN K - THEORY . Given a U ( n ) -bundle over a finite CW complex X there is con- structed an element J ( ) & K ( M ( ) ) where M ( 5 ) ... Isomorphism in K-theory Exterior Algebra.
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Pierre E. Conner, E. E. Floyd. is an isomorphism hk ( X ) ≈ h * + * ( D ( 5 ) , k + n ( D ( K ) , JD ( G ) ) mapping a ... isomorphism KO ( X ) ≈ KO ( M ( K ) ) , and if is an SU ( 4k + 2 ) -bundle over X , we get 5 . KO ( X ) KSP ( M ...
Pierre E. Conner, E. E. Floyd. is an isomorphism hk ( X ) ≈ h * + * ( D ( 5 ) , k + n ( D ( K ) , JD ( G ) ) mapping a ... isomorphism KO ( X ) ≈ KO ( M ( K ) ) , and if is an SU ( 4k + 2 ) -bundle over X , we get 5 . KO ( X ) KSP ( M ...
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... isomorphism so is 1 ° Hence if T is an isomorphism and if E ' ' → X ' ' is trivial ( so that 2 E ' ( E ' ' →→ X'X ' ' is also trivial ) , then T is an isomorphism . 1 The theorem then follows readily . We use Dold's theorem as a ...
... isomorphism so is 1 ° Hence if T is an isomorphism and if E ' ' → X ' ' is trivial ( so that 2 E ' ( E ' ' →→ X'X ' ' is also trivial ) , then T is an isomorphism . 1 The theorem then follows readily . We use Dold's theorem as a ...
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