The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
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... framed bordism groups Ω * ( • ) . Q fr n ( point ) The spectrum - The coefficient group Ω fr are just the stable ... stable tangent bundle T and a given compatible framing of T restricted to the boundary M. These bordism classes have Chern ...
... framed bordism groups Ω * ( • ) . Q fr n ( point ) The spectrum - The coefficient group Ω fr are just the stable ... stable tangent bundle T and a given compatible framing of T restricted to the boundary M. These bordism classes have Chern ...
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... 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 bordism groups Ω U ...
... 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 bordism groups Ω U ...
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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