The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 26
... homotopy classes of base point preserving Given f : X → M , there is the composition ^ Mn ^ X → M ' n + 1 ° → Mn + 1 Define which we also denote by ( X ; M ) = Dir Lim [ sk ^ X , Mo + kd . n It is easily checked that H ( ; M ) is a ...
... homotopy classes of base point preserving Given f : X → M , there is the composition ^ Mn ^ X → M ' n + 1 ° → Mn + 1 Define which we also denote by ( X ; M ) = Dir Lim [ sk ^ X , Mo + kd . n It is easily checked that H ( ; M ) is a ...
Page 105
... homotopy class of cross - sections of SUB1 defined over Β together with a compatible class of cross - sections of U → B1 defined over all of вn . This is independent of m for m large [ 12 , ( 2.3 ) ] . Such a ( U , SU ) -structure ...
... homotopy class of cross - sections of SUB1 defined over Β together with a compatible class of cross - sections of U → B1 defined over all of вn . This is independent of m for m large [ 12 , ( 2.3 ) ] . Such a ( U , SU ) -structure ...
Page
... homotopy groups , and a theorem of Rohlin , Proc . Int . Cong . Math . 1958 , Cambridge ( 1960 ) . 21. S. P. Novikov , Homotopy properties of Thom complexes , Mat . Sb . 57 ( 1962 ) , 407-442 ( Russian ) . 22 . R. S. Palais et al ...
... homotopy groups , and a theorem of Rohlin , Proc . Int . Cong . Math . 1958 , Cambridge ( 1960 ) . 21. S. P. Novikov , Homotopy properties of Thom complexes , Mat . Sb . 57 ( 1962 ) , 407-442 ( Russian ) . 22 . R. S. Palais et al ...
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