The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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... gives rise to a homomorphism Q Td fr EU : : Ω 2n - 1 → Q / 2 . This turns out to coincide with a well - known homomorphism of Adams , fr e : 0 → Q / 2 . с 2n - 1 We are thus able to give a cobordism interpretation of the results of ...
... gives rise to a homomorphism Q Td fr EU : : Ω 2n - 1 → Q / 2 . This turns out to coincide with a well - known homomorphism of Adams , fr e : 0 → Q / 2 . с 2n - 1 We are thus able to give a cobordism interpretation of the results of ...
Page 47
... gives zero . Also consider n Σ i = 0 ( −1 ) 3 π * ( P1 ( 7 ) ) • pn −- 3 , which upon restriction to V gives zero . Since HP ( n ) ΙΣ in h ( HP ( m i = 0 i = UUV , one sees that 1 5 n j ( −1 ) 1 77 * ( P1 ( 3 ) ) p TM −1 ) . ( Σ ...
... gives zero . Also consider n Σ i = 0 ( −1 ) 3 π * ( P1 ( 7 ) ) • pn −- 3 , which upon restriction to V gives zero . Since HP ( n ) ΙΣ in h ( HP ( m i = 0 i = UUV , one sees that 1 5 n j ( −1 ) 1 77 * ( P1 ( 3 ) ) p TM −1 ) . ( Σ ...
Page 97
... ( U , fr ) -manifold . n We could give a complete bordism description of this group , but we forego the tedious details . Given an м2n , n > 0 , and the associated map g : s2n + 2k → MU ( k ) / s2k , there is H2n ( BU ( k ) ) = 19 H2n 97.
... ( U , fr ) -manifold . n We could give a complete bordism description of this group , but we forego the tedious details . Given an м2n , n > 0 , and the associated map g : s2n + 2k → MU ( k ) / s2k , there is H2n ( BU ( k ) ) = 19 H2n 97.
Contents
The Thom Isomorphism in Ktheory | 1 |
Cobordism Characteristic Classes | 38 |
UManifolds with Framed Boundaries | 69 |
Copyright | |
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abelian group algebra base point bordism bordism classes bordism groups bundle map ch+k characteristic classes Chern classes Chern numbers closed U-manifold cobordism cohomology theory complex inner product complex vector space composition consider COROLLARY CP(n CW pair X,A define denote diagram dimension Dold epimorphism fiber finite CW complex finite CW pair fr)-manifold framed manifold Hence homotopy class Hopf HP(n identified induced inner product space integer K-theory kernel KSP(X LEMMA line bundle linear M²n map f Milnor monomial MSU 4k MU(k multiplicative cohomology theory n)-bundle ñ¹ 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 vector space bundle Z-graded εΩ Ωυ