The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 18
... similarly * ( ૬૪ 7 ) = t ( 5 ) × t ( n ) , m m = 4k , n = 47 s ( x = t ( 5 ) × 8 ( 1 ) , m = 4k , n = 47 + 2 t ... Similarly if is a U ( 1 ) -bundle over X , we compute ( 5 ) ɛ K ( M ( ₹ ) ) . So let be an SU ( 2 ) -bundle over X ...
... similarly * ( ૬૪ 7 ) = t ( 5 ) × t ( n ) , m m = 4k , n = 47 s ( x = t ( 5 ) × 8 ( 1 ) , m = 4k , n = 47 + 2 t ... Similarly if is a U ( 1 ) -bundle over X , we compute ( 5 ) ɛ K ( M ( ₹ ) ) . So let be an SU ( 2 ) -bundle over X ...
Page 76
... similarly on homology there is 9 : H12 ( X , A ) ~ Hx + εn ( D ( T ) , D ( ( A ) US ( 5 ) ) . ~ ev k + 2n Denote by H ( X , A ; Q ) the commutative ring Hev ( X , A ; Q ) = - Σ 2k H ( X , A ; Q ) . k > 0 Denote by Hev ( X , A ; Q ) ...
... similarly on homology there is 9 : H12 ( X , A ) ~ Hx + εn ( D ( T ) , D ( ( A ) US ( 5 ) ) . ~ ev k + 2n Denote by H ( X , A ; Q ) the commutative ring Hev ( X , A ; Q ) = - Σ 2k H ( X , A ; Q ) . k > 0 Denote by Hev ( X , A ; Q ) ...
Page 87
... Similarly if = p = ••• = i and hence iii ) follows . If p = S ( M ) ( 1 * [ M ] mod p - = [ M ] mod p p = 1 mod p . Both Stong [ 23 ] and Hattori [ 15 ] have given proofs of the following theorem . We are using Stong's proof here ...
... Similarly if = p = ••• = i and hence iii ) follows . If p = S ( M ) ( 1 * [ M ] mod p - = [ M ] mod p p = 1 mod p . Both Stong [ 23 ] and Hattori [ 15 ] have given proofs of the following theorem . We are using Stong's proof here ...
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