The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
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... manifolds Mn , similarly for SU n and Sp On the other hand there are the • n Grothendieck - Atiyah - Hirzebruch periodic cohomology theories K * ( • ) , K0 * ( - ) of K - theory . The main point of Chapter I , then , is to define ...
... manifolds Mn , similarly for SU n and Sp On the other hand there are the • n Grothendieck - Atiyah - Hirzebruch periodic cohomology theories K * ( • ) , K0 * ( - ) of K - theory . The main point of Chapter I , then , is to define ...
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... manifolds M , where roughly a ( U , fr ) -manifold is a differentiable manifold M with a given complex structure on its stable tangent bundle T and a given compatible framing of T restricted to the boundary M. These bordism classes have ...
... manifolds M , where roughly a ( U , fr ) -manifold is a differentiable manifold M with a given complex structure on its stable tangent bundle T and a given compatible framing of T restricted to the boundary M. These bordism classes have ...
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... manifold M2 , there is a closed weakly almost complex manifold having the same Chern numbers 2n 2n as M if and only if Td [ M ] is an integer ; this makes use of re- cent theorems of Stong [ 23 ] and Hattori [ 15 ] . There is a diagram ...
... manifold M2 , there is a closed weakly almost complex manifold having the same Chern numbers 2n 2n as M if and only if Td [ M ] is an integer ; this makes use of re- cent theorems of Stong [ 23 ] and Hattori [ 15 ] . There is a diagram ...
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... Manifolds with Framed Boundaries 69 12. The U - bordism groups U * 70 13. Characteristic numbers from K - theory 78 14. The theorem of Stong and Hattori 82 SU 17. The groups , 15. U - manifolds with stably framed boundaries 16. The ...
... Manifolds with Framed Boundaries 69 12. The U - bordism groups U * 70 13. Characteristic numbers from K - theory 78 14. The theorem of Stong and Hattori 82 SU 17. The groups , 15. U - manifolds with stably framed boundaries 16. The ...
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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