The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
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... similarly for SU n and Sp On the other hand there are the • n Grothendieck - Atiyah - Hirzebruch periodic cohomology theories K * ( • ) , K0 * ( - ) of K - theory . The main point of Chapter I , then , is to define natural ...
... similarly for SU n and Sp On the other hand there are the • n Grothendieck - Atiyah - Hirzebruch periodic cohomology theories K * ( • ) , K0 * ( - ) of K - theory . The main point of Chapter I , then , is to define natural ...
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... Similarly symplectic cobordism determines * KO ̊ ( • ) . The isomorphisms are generated by respectively . Various topics are treated along the way , in particular cobordism characteristic classes . There is the sphere spectrum , whose ...
... Similarly symplectic cobordism determines * KO ̊ ( • ) . The isomorphisms are generated by respectively . Various topics are treated along the way , in particular cobordism characteristic classes . There is the sphere spectrum , whose ...
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... 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 ( 5 ) ) . These Thom classes give rise to isomorphisms K ...
... 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 ( 5 ) ) . These Thom classes give rise to isomorphisms K ...
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... similarly define Rody Let Ʌody = Σ 2k + 1v , ^ Σ1 nev v = and Revv . V If n = 2 mod 4 then SU ( n ) od ет spaces V and ^ v . 2k V ; acts on the quaternionic vector If n = 0 mod 4 then SU ( n ) acts on the real vector spaces Rody and Rev ...
... similarly define Rody Let Ʌody = Σ 2k + 1v , ^ Σ1 nev v = and Revv . V If n = 2 mod 4 then SU ( n ) od ет spaces V and ^ v . 2k V ; acts on the quaternionic vector If n = 0 mod 4 then SU ( n ) acts on the real vector spaces Rody and Rev ...
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... similarly an isomorphism R AW ≈ ( V + W ) of quaternionic vector spaces , where q & H acts on the left hand side by 10 q . Consider finally the case m = 4k + 2 , n = 4X + 2. Define a left action of H on AW by q⚫Y = Y.q , so that we ...
... similarly an isomorphism R AW ≈ ( V + W ) of quaternionic vector spaces , where q & H acts on the left hand side by 10 q . Consider finally the case m = 4k + 2 , n = 4X + 2. Define a left action of H on AW by q⚫Y = Y.q , so that we ...
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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