The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 31
... induced by U ( n - 1 ) C U ( n ) ( see Borel [ 8 ] ) may be taken to be the sphere bundle over BU ( n ) ... induces * 1 * : Hˆ ( MU ( n ) ) = Ci , i < n , → H * ( BU ( n ) ) which maps H * ( MU ( n ) ) isomorphically onto the ideal of H ...
... induced by U ( n - 1 ) C U ( n ) ( see Borel [ 8 ] ) may be taken to be the sphere bundle over BU ( n ) ... induces * 1 * : Hˆ ( MU ( n ) ) = Ci , i < n , → H * ( BU ( n ) ) which maps H * ( MU ( n ) ) isomorphically onto the ideal of H ...
Page 32
... inducing inducing f : M ( 5 ) : M ( 5 ) → E ( 5 ) → E ( ɲ ) is a → E ( 7 ) M ( Ŋ ) and a map M ( 7 ) F : X → Y of base spaces , then commutativity holds in * ( Y ) * H * ( x ) ول ф Hk + 2n ( x ( 7 ) ) → Hk + 2n ( M ( 5 ) ) . Also ...
... inducing inducing f : M ( 5 ) : M ( 5 ) → E ( 5 ) → E ( ɲ ) is a → E ( 7 ) M ( Ŋ ) and a map M ( 7 ) F : X → Y of base spaces , then commutativity holds in * ( Y ) * H * ( x ) ول ф Hk + 2n ( x ( 7 ) ) → Hk + 2n ( M ( 5 ) ) . Also ...
Page 105
... induces a natural SU - structure on B1 of course . Note that the cross - section of Bn induces a principal U ( 1 ) -bundle over Bn , which along Bn already has a homotopy class of cross - sections ; thus , the first Chern class c1 ( B ) ...
... induces a natural SU - structure on B1 of course . Note that the cross - section of Bn induces a principal U ( 1 ) -bundle over Bn , which along Bn already has a homotopy class of cross - sections ; thus , the first Chern class c1 ( B ) ...
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