The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
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... isomorphism : AV → AV with ' 1 ^ • A V Λ ... AV k ^ 1 = ( -1 ) k ( k - 1 ) / 2 k It is clear that is unitary . DEFINITION . By an SU - structure for V we shall mean a unit vector σε V ; suppose an SU - structure has been fixed for V ...
... isomorphism : AV → AV with ' 1 ^ • A V Λ ... AV k ^ 1 = ( -1 ) k ( k - 1 ) / 2 k It is clear that is unitary . DEFINITION . By an SU - structure for V we shall mean a unit vector σε V ; suppose an SU - structure has been fixed for V ...
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... isomorphisms are taken to be real linear , while in cases 2 and 3 they are taken to be quaternionic linear . For each v 0 in V we also obtain isomorphisms od ev . 9 ̧ : ^ ° dv≈ 1 © 5 сл Cobordism and homomorphisms into K-theory.
... isomorphisms are taken to be real linear , while in cases 2 and 3 they are taken to be quaternionic linear . For each v 0 in V we also obtain isomorphisms od ev . 9 ̧ : ^ ° dv≈ 1 © 5 сл Cobordism and homomorphisms into K-theory.
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... isomorphism R AW ≈ ( V + W ) of quaternionic vector spaces , where q & H acts on the left hand side by 10 q . Consider finally the case m = 4k + 2 , n = 4X + 2. Define a left action of H on AW by q⚫Y = Y.q , so that we obtain a real ...
... isomorphism R AW ≈ ( V + W ) of quaternionic vector spaces , where q & H acts on the left hand side by 10 q . Consider finally the case m = 4k + 2 , n = 4X + 2. Define a left action of H on AW by q⚫Y = Y.q , so that we obtain a real ...
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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