The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 69
... stable tangent bundle . In section 13 we begin to study the numbers x [ M ] < ch x • T ̃2 ( M ) , σ ( M ) > = where x ɛ K ( M ) , T − 1 ( M ) is the Todd polynomial of M and ☛ ( M ) ɛ H ̧ ( M ) is the orientation class . In particular ...
... stable tangent bundle . In section 13 we begin to study the numbers x [ M ] < ch x • T ̃2 ( M ) , σ ( M ) > = where x ɛ K ( M ) , T − 1 ( M ) is the Todd polynomial of M and ☛ ( M ) ɛ H ̧ ( M ) is the orientation class . In particular ...
Page 78
... stable tangent bundle T + ( 2k equivalence . Denote by ' = X ' ( M ) ε X ' n ) is then a complex vector space bundle , unique up to T ' ( M ) ɛ K ( M2 ) the element represented by this complex bundle . Then let T ( M2 ) = T ( T ' ) , T2 ...
... stable tangent bundle T + ( 2k equivalence . Denote by ' = X ' ( M ) ε X ' n ) is then a complex vector space bundle , unique up to T ' ( M ) ɛ K ( M2 ) the element represented by this complex bundle . Then let T ( M2 ) = T ( T ' ) , T2 ...
Page 93
... vector space bundle , when restricted to aм " . - Denote by the stable tangent bundle of м " , a bundle of k - dimensional complex vector spaces . Moreover we are given an isomorphism of ' am with the trivial bundle k on aм ...
... vector space bundle , when restricted to aм " . - Denote by the stable tangent bundle of м " , a bundle of k - dimensional complex vector spaces . Moreover we are given an isomorphism of ' am with the trivial bundle k on aм ...
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