The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 68
... Adams [ 3 ] , the right hand side is as stated and the assertion follows . In a later section we give a bordism proof of the theorem of Adams . CHAPTER III . U - MANIFOLDS WITH FRAMED BOUNDARIES In 68.
... Adams [ 3 ] , the right hand side is as stated and the assertion follows . In a later section we give a bordism proof of the theorem of Adams . CHAPTER III . U - MANIFOLDS WITH FRAMED BOUNDARIES In 68.
Page 100
... Adams defines ec ( a ) = r mod 1 ɛ Q / Z . We give a proof due to P. S. Landweber of the following theorem ; it replaces a more awkward proof of our own . ( 16.2 ) Ω THEOREM . Using the natural identifications fr 2n - 1 ≈ π ᅲ 2n + 2k ...
... Adams defines ec ( a ) = r mod 1 ɛ Q / Z . We give a proof due to P. S. Landweber of the following theorem ; it replaces a more awkward proof of our own . ( 16.2 ) Ω THEOREM . Using the natural identifications fr 2n - 1 ≈ π ᅲ 2n + 2k ...
Page 102
... Adams [ 3 ] which completely analyze the image of e , C note by B the nth Bernoulli number . n For each positive integer n , de- Denote by an the denominator of B / 4n in lowest terms ( for references , see [ 2,20 ] ) . n Let dan = a2n ...
... Adams [ 3 ] which completely analyze the image of e , C note by B the nth Bernoulli number . n For each positive integer n , de- Denote by an the denominator of B / 4n in lowest terms ( for references , see [ 2,20 ] ) . n Let dan = a2n ...
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