The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 54
... Proof . We may use the proof of ( 8.1 ) , making suitable replace- ments including the replacement of μ by ph . In order to use that proof , we need ph Z There is the natural diagram s4n + 3 f CP ( 2n + 1 ) HP ( n ) from which it ...
... Proof . We may use the proof of ( 8.1 ) , making suitable replace- ments including the replacement of μ by ph . In order to use that proof , we need ph Z There is the natural diagram s4n + 3 f CP ( 2n + 1 ) HP ( n ) from which it ...
Page 63
... Proof . With a crucial change , the proof is quite similar to the proof of ( 10.1 ) . The minor changes we leave to the reader , and go directly to the critical point . Note that the proof of ( 10.1 ) pro- ceeded in three stages . While ...
... Proof . With a crucial change , the proof is quite similar to the proof of ( 10.1 ) . The minor changes we leave to the reader , and go directly to the critical point . Note that the proof of ( 10.1 ) pro- ceeded in three stages . While ...
Page 100
... 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 - 1 ( s2k ) ≈ { s2n - 1 , so } for 2k large , the ...
... 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 - 1 ( s2k ) ≈ { s2n - 1 , so } for 2k large , the ...
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