The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 69
... fr ) -manifold . Such a manifold M has a complex structure on its stable tangent bundle together with a compatible framing of the restriction OM to the boundary . Such manifolds have Chern classes and Chern numbers , hence also a Todd ...
... fr ) -manifold . Such a manifold M has a complex structure on its stable tangent bundle together with a compatible framing of the restriction OM to the boundary . Such manifolds have Chern classes and Chern numbers , hence also a Todd ...
Page 93
... fr ) -manifold is a triple ( M2 , § , e ) consisting of a diffe- rentiable manifold M , a U - structure on and a stable framing e of ǝ such that ea . Many non - trivial examples exist by virtue of the above construction . Picking ...
... fr ) -manifold is a triple ( M2 , § , e ) consisting of a diffe- rentiable manifold M , a U - structure on and a stable framing e of ǝ such that ea . Many non - trivial examples exist by virtue of the above construction . Picking ...
Page 103
... fr U u U , fr Ωυ , 2 a fr 0 , 2n 2n 2n - 1 to be the image under of Tor QU , fr · It is 2n - 1 2n ε easily verified that e D if and only if given [ ne ( U , fr 2n 2n with [ M2n ] = there exists a closed U - manifold having the same Now @ ...
... fr U u U , fr Ωυ , 2 a fr 0 , 2n 2n 2n - 1 to be the image under of Tor QU , fr · It is 2n - 1 2n ε easily verified that e D if and only if given [ ne ( U , fr 2n 2n with [ M2n ] = there exists a closed U - manifold having the same Now @ ...
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