The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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... Todd genus Td : " → z . 2n In Chapter II we show among other things that the cobordism theories determine the K - theories . For example , μ generates a ring homomorphism Q → Z and makes Z into a * -module . It is shown that * U * K ...
... Todd genus Td : " → z . 2n In Chapter II we show among other things that the cobordism theories determine the K - theories . For example , μ generates a ring homomorphism Q → Z and makes Z into a * -module . It is shown that * U * K ...
Page 37
... Todd genus of м2n as in Hirzebruch . 2n Consider a stable tangent bundle for M where M2n s2n + 2k as above . Proof . 2n Μ J ( 5 + Y ) Since + is trivial , then 1/7 ( 5 ) . That is , σ 7 2n = 7 ( 5 ) 7 ( 7 ) = 1 , hence ( 7 ) = = the ...
... Todd genus of м2n as in Hirzebruch . 2n Consider a stable tangent bundle for M where M2n s2n + 2k as above . Proof . 2n Μ J ( 5 + Y ) Since + is trivial , then 1/7 ( 5 ) . That is , σ 7 2n = 7 ( 5 ) 7 ( 7 ) = 1 , hence ( 7 ) = = the ...
Page 66
... Todd genus T [ M ] = 1 8n 8n 8n εΩ 8n 1 according to ( 6.5 ) . It is then sufficient to switch to bordism . SU Denote by the bordism ring of closed SU - manifolds ( denoted by in [ 12 ] ) . We 8n must prove that if [ Mon ) e ( ) SU 8n ...
... Todd genus T [ M ] = 1 8n 8n 8n εΩ 8n 1 according to ( 6.5 ) . It is then sufficient to switch to bordism . SU Denote by the bordism ring of closed SU - manifolds ( denoted by in [ 12 ] ) . We 8n must prove that if [ Mon ) e ( ) SU 8n ...
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