The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
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... respectively . Various topics are treated along the way , in particular cobordism characteristic classes . There is the sphere spectrum , whose homology groups are the fr framed bordism groups Ω * ( • ) . Q fr n ( point ) The spectrum ...
... respectively . Various topics are treated along the way , in particular cobordism characteristic classes . There is the sphere spectrum , whose homology groups are the fr framed bordism groups Ω * ( • ) . Q fr n ( point ) The spectrum ...
Page 5
... 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 consider AV as a Z - graded ...
... 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 consider AV as a Z - graded ...
Page 6
... respectively . Proof . Fix an orthonormal basis em + n for W such that e for V and 1 m em + 1 e1 Л ле e ле em + n 2 * By ( 1.1 ) , TX is the unique monomial X with X ^ X = 1 = σ 2 ° the unique monomial Y with Y A Y = σ Then ( X ^ X ) ...
... respectively . Proof . Fix an orthonormal basis em + n for W such that e for V and 1 m em + 1 e1 Л ле e ле em + n 2 * By ( 1.1 ) , TX is the unique monomial X with X ^ X = 1 = σ 2 ° the unique monomial Y with Y A Y = σ Then ( X ^ X ) ...
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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