The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 30
... bundle space of a right principal U ( n ) -bundle over a space X. The associated sphere bundle is given by E ( § ) × ( U ( n ) / U ( n − 1 ) ) / U ( n ) → X. There is an identification E ( 3 ) ... U ( n - 1 ) of U ( n 30 The homomorphism c.
... bundle space of a right principal U ( n ) -bundle over a space X. The associated sphere bundle is given by E ( § ) × ( U ( n ) / U ( n − 1 ) ) / U ( n ) → X. There is an identification E ( 3 ) ... U ( n - 1 ) of U ( n 30 The homomorphism c.
Page 31
Pierre E. Conner, E. E. Floyd. U ( n - 1 ) of U ( n ) , hence E ( ) / U ( n − 1 ) the natural map - → = BU ( n - 1 ) ... bundle over BU ( n ) . Considering the pair ( D ( F ) , S ( F ) ) , we get the exact cohomology sequence 5 10 ...
Pierre E. Conner, E. E. Floyd. U ( n - 1 ) of U ( n ) , hence E ( ) / U ( n − 1 ) the natural map - → = BU ( n - 1 ) ... bundle over BU ( n ) . Considering the pair ( D ( F ) , S ( F ) ) , we get the exact cohomology sequence 5 10 ...
Page 48
... ( n ) ) is a free h - module with basis ( b ) inclusion i : CP ( n ) CCP ( n + 1 ) has i n lr , = γ n n + 1 n : Then there exists a unique function assigning to each U ( m ) -bundle ... bundle map f : 3 → spaces has * ( n ) = c ( 5 ) , ...
... ( n ) ) is a free h - module with basis ( b ) inclusion i : CP ( n ) CCP ( n + 1 ) has i n lr , = γ n n + 1 n : Then there exists a unique function assigning to each U ( m ) -bundle ... bundle map f : 3 → spaces has * ( n ) = c ( 5 ) , ...
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