The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
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Page 1
... obtained . Formulas for the Chern character ch J ( 3 ) are No claims for originality are made in this chapter ; the methods have been well - known since the work of Atiyah - Hirzebruch [ 6 ] , Dold [ 13 ] , and others [ 7 ] . However ...
... obtained . Formulas for the Chern character ch J ( 3 ) are No claims for originality are made in this chapter ; the methods have been well - known since the work of Atiyah - Hirzebruch [ 6 ] , Dold [ 13 ] , and others [ 7 ] . However ...
Page 5
... obtain a Z - graded real vector space RV . A main purpose of this section is to prove the following . ( 2.1 ) THEOREM . There exist natural isomorphisms R ( V + W ) ≈ R ( V ) ✪ R ( W ) , m = 4k , n = 4X R ^ ( V + W ) ~ R ( V ) ...
... obtain a Z - graded real vector space RV . A main purpose of this section is to prove the following . ( 2.1 ) THEOREM . There exist natural isomorphisms R ( V + W ) ≈ R ( V ) ✪ R ( W ) , m = 4k , n = 4X R ^ ( V + W ) ~ R ( V ) ...
Page 7
... obtain a real vector space AV AW . H and define q Here we write an element q as + j where α , ßɛ c ε - ; this is an anti - automorphism of H. There is a natural epimorphism AV d ' : ^ V R ^ w → Av R ® C 1W . H If X ε AV and Y ɛ Aw ...
... obtain a real vector space AV AW . H and define q Here we write an element q as + j where α , ßɛ c ε - ; this is an anti - automorphism of H. There is a natural epimorphism AV d ' : ^ V R ^ w → Av R ® C 1W . H If X ε AV and Y ɛ Aw ...
Page 12
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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