The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
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Page 1
... dimension n , and we also fix a unit vector & V. If n = 4k + 2 , we make the exterior algebra AV into a quaternionic vector space . If n = 4k then a real vector subspace RV of The Thom Isomorphism in K-theory Exterior Algebra.
... dimension n , and we also fix a unit vector & V. If n = 4k + 2 , we make the exterior algebra AV into a quaternionic vector space . If n = 4k then a real vector subspace RV of The Thom Isomorphism in K-theory Exterior Algebra.
Page 2
... dimension n . To fit with quaternionic notation , the complex numbers are taken to act on the right and the inner product < , > is taken conjugate linear in the first variable and complex linear in the second . n There is the graded ...
... dimension n . To fit with quaternionic notation , the complex numbers are taken to act on the right and the inner product < , > is taken conjugate linear in the first variable and complex linear in the second . n There is the graded ...
Page 4
... dimension n , with given SU - structure . If n = 4k + 2 then AV becomes a right quaternionic vector space by defining Y⚫j = ( Y ) for Y & ɅV . Moreover SU ( n ) acts on AV in a quaternionic linear fashion . If n = 4k , let R ( V ) be ...
... dimension n , with given SU - structure . If n = 4k + 2 then AV becomes a right quaternionic vector space by defining Y⚫j = ( Y ) for Y & ɅV . Moreover SU ( n ) acts on AV in a quaternionic linear fashion . If n = 4k , let R ( V ) be ...
Page 5
... dimension and o Using the m , n respectively , with given SU - structures o identification A ( V + W ) = 1 2 AVAW of graded algebras , then V + W receives the SU - structure σ = σ ∞ σ According to section 1 , if 1 2 m = 2 mod 4 we ...
... dimension and o Using the m , n respectively , with given SU - structures o identification A ( V + W ) = 1 2 AVAW of graded algebras , then V + W receives the SU - structure σ = σ ∞ σ According to section 1 , if 1 2 m = 2 mod 4 we ...
Page 7
... dimension , then RV RW R ( VW ) . R Since It is also seen that the actions of SU ( m ) × SU ( n ) on the two sides are identified . RV If m = 4k and n = 47 + 2 then one sets up similarly an isomorphism R AW ≈ ( V + W ) of quaternionic ...
... dimension , then RV RW R ( VW ) . R Since It is also seen that the actions of SU ( m ) × SU ( n ) on the two sides are identified . RV If m = 4k and n = 47 + 2 then one sets up similarly an isomorphism R AW ≈ ( V + W ) of quaternionic ...
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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