The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
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... Thom isomorphism in K - theory . The families U , SU , Sp of unitary , special unitary , symplectic groups generate spectra MU , MSU , MSp of Thom spaces . In the fashion of G. W. Whitehead [ 26 ] , each spectrum generates a generalized ...
... Thom isomorphism in K - theory . The families U , SU , Sp of unitary , special unitary , symplectic groups generate spectra MU , MSU , MSp of Thom spaces . In the fashion of G. W. Whitehead [ 26 ] , each spectrum generates a generalized ...
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... cobordism completely ; this is because of our ignorance . However the recent work of Anderson- Brown - Peterson is a notable example of the application of K - theory to cobordism . CONTENTS Chapter I. The Thom Isomorphism in K - theory.
... cobordism completely ; this is because of our ignorance . However the recent work of Anderson- Brown - Peterson is a notable example of the application of K - theory to cobordism . CONTENTS Chapter I. The Thom Isomorphism in K - theory.
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P. E. Conner, E. E. Floyd. CONTENTS Chapter I. The Thom Isomorphism in K - theory . 1. Exterior Algebra ... 2. Tensor products of exterior algebras 3. Application to bundles 4. Thom classes of line bundles 5. Cobordism and homomorphisms ...
P. E. Conner, E. E. Floyd. CONTENTS Chapter I. The Thom Isomorphism in K - theory . 1. Exterior Algebra ... 2. Tensor products of exterior algebras 3. Application to bundles 4. Thom classes of line bundles 5. Cobordism and homomorphisms ...
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... Thom space of § ; we call J ( 5 ) the Thom class of § . Similarly given an SU ( 4k ) -bundle there is constructed a Thom class t ( 3 ) ɛ KO ( M ( 5 ) ) , and given an SU ( 4k + 2 ) -bundle there is constructed a class s ( 5 ) & KSp ( M ...
... Thom space of § ; we call J ( 5 ) the Thom class of § . Similarly given an SU ( 4k ) -bundle there is constructed a Thom class t ( 3 ) ɛ KO ( M ( 5 ) ) , and given an SU ( 4k + 2 ) -bundle there is constructed a class s ( 5 ) & KSp ( M ...
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... action of the quaternions H on AV , and AV is a quaternionic vector space . Consider g ɛ SU ( n ) . Then 8 ( X ) ) = b / M ( X ) = / 8 ( X ) g 48 ( X ) = ( gX ) j n = 4k , we have μ2 using ( 1.4 Thom classes of line bundles.
... action of the quaternions H on AV , and AV is a quaternionic vector space . Consider g ɛ SU ( n ) . Then 8 ( X ) ) = b / M ( X ) = / 8 ( X ) g 48 ( X ) = ( gX ) j n = 4k , we have μ2 using ( 1.4 Thom classes of line bundles.
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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