The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
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... proved that given a compact ( U , fr ) -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 ] ...
... proved that given a compact ( U , fr ) -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 ] ...
Page 3
... prove ( 1.2 ) for monomials . monomial , TX is the unique monomial with XA TX = σ . Tx ^ x = ( -1 ) k ( n - k ) σ and Define an operator μ : ^ kv conjugate linear . 2x ( −1 ) k ( n − k ) x . For X a → ^ n - ky by μ = TL . Thenμ is ...
... prove ( 1.2 ) for monomials . monomial , TX is the unique monomial with XA TX = σ . Tx ^ x = ( -1 ) k ( n - k ) σ and Define an operator μ : ^ kv conjugate linear . 2x ( −1 ) k ( n − k ) x . For X a → ^ n - ky by μ = TL . Thenμ is ...
Page 5
... proved . v = y ; similarly define Rody Let Ʌody = Σ 2k + 1v , ^ Σ1 nev v = and Revv . V If n = 2 mod 4 then SU ( n ) ... prove the following . ( 2.1 ) THEOREM . There exist natural isomorphisms R ( V + W ) ≈ R ( V ) ✪ R ( W ) , m = 4k ...
... proved . v = y ; similarly define Rody Let Ʌody = Σ 2k + 1v , ^ Σ1 nev v = and Revv . V If n = 2 mod 4 then SU ( n ) ... prove the following . ( 2.1 ) THEOREM . There exist natural isomorphisms R ( V + W ) ≈ R ( V ) ✪ R ( W ) , m = 4k ...
Page 8
... proved . H Return now to a single complex inner product space V of finite dimension . Given v ɛ V there is F F F ( X ) V : AV → AV defined by = V ^ X. There is also its adjoint ( F ) * : ^ V → AV defined by < X , FY > = < F * X , Y > ...
... proved . H Return now to a single complex inner product space V of finite dimension . Given v ɛ V there is F F F ( X ) V : AV → AV defined by = V ^ X. There is also its adjoint ( F ) * : ^ V → AV defined by < X , FY > = < F * X , Y > ...
Page 24
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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