The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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... coefficient groups are , taking one case N * n = U U ( point ) , Ω U = 125 ( point ) and are n n U n Moreover is just the bordism group of all closed weakly almost complex manifolds мn , Sp . on the other hand there are the n ...
... coefficient groups are , taking one case N * n = U U ( point ) , Ω U = 125 ( point ) and are n n U n Moreover is just the bordism group of all closed weakly almost complex manifolds мn , Sp . on the other hand there are the n ...
Page 49
... coefficient ring ( * has ( -2n CNU the U U U cobordism group of closed weakly 2n complex manifolds of dimension 2n ... coefficient * group has been determined [ 12 ] ; few computations have been made Ω for Q * SU ( x ) . The structure of ...
... coefficient ring ( * has ( -2n CNU the U U U cobordism group of closed weakly 2n complex manifolds of dimension 2n ... coefficient * group has been determined [ 12 ] ; few computations have been made Ω for Q * SU ( x ) . The structure of ...
Page 80
... coefficient of th in the above is one , and thus that Td [ CP ( n ) ] = 1 . - = Let x = ( 1 - p ) where is the Hopf bundle and 0 ≤ k ≤ n . ) k Then ch x • T− ( CP ( n ) ) n + 1 = - ( 1 − e − t ) k ( t / ( 1 − e − t ) ) - = tk ( t ...
... coefficient of th in the above is one , and thus that Td [ CP ( n ) ] = 1 . - = Let x = ( 1 - p ) where is the Hopf bundle and 0 ≤ k ≤ n . ) k Then ch x • T− ( CP ( n ) ) n + 1 = - ( 1 − e − t ) k ( t / ( 1 − e − t ) ) - = tk ( t ...
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