The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 2
... basis for V then the e erl form an orthonormal basis for v . There is also a canonical anti - isomorphism : AV with r1 <く AVAV with ለ ∞ ( * _ ^ • • • ^ %% ) = V , A = ( -1 ) * ( k - 1 ) / 2 + , Κ It is clear that is unitary ...
... basis for V then the e erl form an orthonormal basis for v . There is also a canonical anti - isomorphism : AV with r1 <く AVAV with ለ ∞ ( * _ ^ • • • ^ %% ) = V , A = ( -1 ) * ( k - 1 ) / 2 + , Κ It is clear that is unitary ...
Page 44
... basis and the theorem holds in case the fibring is trivial . n Consider next the general case . Let X ' be a subcomplex of X · π - 1 and let E ' = π ( X ' ) . Let M be a free h - module with basis · Define n by ( ac ) = T : h ( x ) M ...
... basis and the theorem holds in case the fibring is trivial . n Consider next the general case . Let X ' be a subcomplex of X · π - 1 and let E ' = π ( X ' ) . Let M be a free h - module with basis · Define n by ( ac ) = T : h ( x ) M ...
Page 64
... basis for the free abelian group H * ( BSp ( n ) ) . It then will follow , using the methods * i of [ 10 , p . 49 ] , that N Sp ( BSp ( n ) — Hˆ ( BSp ) ® N Sp The universal bundle over BSP ( n ) has Chern classes C2 , C4 , * It is ...
... basis for the free abelian group H * ( BSp ( n ) ) . It then will follow , using the methods * i of [ 10 , p . 49 ] , that N Sp ( BSp ( n ) — Hˆ ( BSp ) ® N Sp The universal bundle over BSP ( n ) has Chern classes C2 , C4 , * It is ...
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