The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
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Page 7
... Define a left action of H on AW by q⚫Y = Y.q , so that we obtain a real vector space AV AW . H and define q Here we write an element q as + j where α , ßɛ c ε - ; this is an anti - automorphism of H. There is a natural epimorphism AV d ...
... Define a left action of H on AW by q⚫Y = Y.q , so that we obtain a real vector space AV AW . H and define q Here we write an element q as + j where α , ßɛ c ε - ; this is an anti - automorphism of H. There is a natural epimorphism AV d ...
Page 8
... Define 9 : AV → AV by 9 . F + ( F _ ) * . V V V V ( 2.3 ) Let V and W be complex inner product spaces , let v ɛ V , w ɛ W and consider v + w ɛ V + W. Using the identification Ʌ ( v + W ) : = AV✪ AW , we have 9т ( XY ) = 9 XO Y + ( -1 ) ...
... Define 9 : AV → AV by 9 . F + ( F _ ) * . V V V V ( 2.3 ) Let V and W be complex inner product spaces , let v ɛ V , w ɛ W and consider v + w ɛ V + W. Using the identification Ʌ ( v + W ) : = AV✪ AW , we have 9т ( XY ) = 9 XO Y + ( -1 ) ...
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abelian group algebra base point bordism bordism classes BSp(n bundle map c₁ ch+k characteristic classes Chern classes Chern numbers closed U-manifold cobordism coefficient groups cohomology theory complex inner product complex vector space consider COROLLARY CP(n CW pair X,A define denote diagram dimension Dold element epimorphism ɛ K(M finite CW complex finite CW pair framed manifold Hence Hirzebruch homotopy class Hopf HP(n identified induced inner product space integer K-theory kernel KSP(X LEMMA line bundle M²n map f module monomial MSU 4k MU(k multiplicative cohomology theory n+2k 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 unitary vector space bundle Z-graded εΩ Ωυ हु