The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 48
... ( CP ( n ) ) such that ( a ) n h ^ ( CP ( 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 over a finite CW ...
... ( CP ( n ) ) such that ( a ) n h ^ ( CP ( 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 over a finite CW ...
Page 80
... [ CP ( n ) ] where x ranges . over the elements of K ( CP ( n ) ) . Note that T ( CP ( n ) ) = ( t / ( 1 1 e ̄t ) , n + 1 where t is the appropriate generator of H2 ( CP ( n ) ) . We assume the fact ( see Hirzebruch [ 16 ] ) that the ...
... [ CP ( n ) ] where x ranges . over the elements of K ( CP ( n ) ) . Note that T ( CP ( n ) ) = ( t / ( 1 1 e ̄t ) , n + 1 where t is the appropriate generator of H2 ( CP ( n ) ) . We assume the fact ( see Hirzebruch [ 16 ] ) that the ...
Page 83
... [ CP ( n ) ] = 2 ( n + 1 ) ! rı ! · · · rs ! ( n + 1 - , s repeated rs times , then The tangent bundle of CP ( n ) is given by T + 1 = ( n + 1 ) 3,5 = } n ( 42 + 4 ) . ··· + hence ω sw ( ~ ) = { $ 112 ( 3 ) ૬ ) S ( 5 ) , there being ( n ...
... [ CP ( n ) ] = 2 ( n + 1 ) ! rı ! · · · rs ! ( n + 1 - , s repeated rs times , then The tangent bundle of CP ( n ) is given by T + 1 = ( n + 1 ) 3,5 = } n ( 42 + 4 ) . ··· + hence ω sw ( ~ ) = { $ 112 ( 3 ) ૬ ) S ( 5 ) , there being ( n ...
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