The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 69
... Chern classes and Chern numbers , hence also a Todd genus Td [ M ] which is now a rational 2n M number . It is proved that if м2n is a compact ( U , fr ) -manifold , then there exists a closed U - manifold with the same Chern numbers Td ...
... Chern classes and Chern numbers , hence also a Todd genus Td [ M ] which is now a rational 2n M number . It is proved that if м2n is a compact ( U , fr ) -manifold , then there exists a closed U - manifold with the same Chern numbers Td ...
Page 74
... Chern numbers . This number is also 2n denoted by $ 11 ' [ M2n ] . According to Milnor , if 2n is not of the ' i p form 2pk 2 for p a prime then there exists a closed U - manifold M2n - s2 [ m2n ] with s . S n = p . k = 1. If 2n = 2p ...
... Chern numbers . This number is also 2n denoted by $ 11 ' [ M2n ] . According to Milnor , if 2n is not of the ' i p form 2pk 2 for p a prime then there exists a closed U - manifold M2n - s2 [ m2n ] with s . S n = p . k = 1. If 2n = 2p ...
Page 98
... Chern numbers , namely * * _1 < 8 * 9 * ¶ ( C11 ••• C1y ) , σ ( s2n + 2k ) > = < ¤11 ( 7 ) • • • Cix ( N ) , o ( M ) > where T + n = 0. Since the Chern numbers Cj1 ••• j , [ M ] can be expressed r in terms of the normal Chern numbers ...
... Chern numbers , namely * * _1 < 8 * 9 * ¶ ( C11 ••• C1y ) , σ ( s2n + 2k ) > = < ¤11 ( 7 ) • • • Cix ( N ) , o ( M ) > where T + n = 0. Since the Chern numbers Cj1 ••• j , [ M ] can be expressed r in terms of the normal Chern numbers ...
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