The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 39
... theorem of Dold . ~ In this section we state and prove a theorem of Dold [ 13 ] which generalizes to an arbitrary multiplicative cohomology theory the Leray - Hirsch theorem on fiberings . As a consequence we obtain uniqueness and ...
... theorem of Dold . ~ In this section we state and prove a theorem of Dold [ 13 ] which generalizes to an arbitrary multiplicative cohomology theory the Leray - Hirsch theorem on fiberings . As a consequence we obtain uniqueness and ...
Page 42
... theorem can be proved just as was a similar theorem in our previous work [ 10 ] . ( 7.3 ) THEOREM . Let h ( ) be a multiplicative cohomology theory . Also let X and Y be finite CW complexes such that h ( Y ) is a free h - module . Then ...
... theorem can be proved just as was a similar theorem in our previous work [ 10 ] . ( 7.3 ) THEOREM . Let h ( ) be a multiplicative cohomology theory . Also let X and Y be finite CW complexes such that h ( Y ) is a free h - module . Then ...
Page 45
... theorem then follows readily . We use Dold's theorem as a basic device in constructing characteristic classes . The following two theorems give the generalities . ( 7.5 ) THEOREM . Let h ( ) be a multiplicative cohomology theory Suppose ...
... theorem then follows readily . We use Dold's theorem as a basic device in constructing characteristic classes . The following two theorems give the generalities . ( 7.5 ) THEOREM . Let h ( ) be a multiplicative cohomology theory Suppose ...
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