The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 49
... ring ( * has ( -2n CNU the U U U cobordism group of closed weakly 2n complex manifolds of dimension 2n . * Hence Q is a polynomial ring U over the integers with one generator in each dimension -2n ( Milnor [ 19 ] , Novikov [ 21 ] ) . In ...
... ring ( * has ( -2n CNU the U U U cobordism group of closed weakly 2n complex manifolds of dimension 2n . * Hence Q is a polynomial ring U over the integers with one generator in each dimension -2n ( Milnor [ 19 ] , Novikov [ 21 ] ) . In ...
Page 59
... ring Kˆ ( X , A ) knowing only the graded algebra ( X , A ) over the module N * ( X , A ) Ω Ω * U In fact , K * ( X , A ) ~ ( * ( X , A ) ® * Z where Z is a * -ring in a natural way . In a similar fashion , * ( X , A ) determines KO ...
... ring Kˆ ( X , A ) knowing only the graded algebra ( X , A ) over the module N * ( X , A ) Ω Ω * U In fact , K * ( X , A ) ~ ( * ( X , A ) ® * Z where Z is a * -ring in a natural way . In a similar fashion , * ( X , A ) determines KO ...
Page 66
... ring ( * . SU Proof . The proof is based on our previous paper [ 12 ] . First we have to convert the statement to one in terms of bordism . According to section 5 , -8n ( - ) U ε SU N * ( • ) U K2 KO * ( • ) + Kc → K ^ ( . ) -3n has ...
... ring ( * . SU Proof . The proof is based on our previous paper [ 12 ] . First we have to convert the statement to one in terms of bordism . According to section 5 , -8n ( - ) U ε SU N * ( • ) U K2 KO * ( • ) + Kc → K ^ ( . ) -3n has ...
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