The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 11
... associated two real vector space bundles Rod ( ' ) and Rev ( ' ) over D ( 5 ) , where D ( 5 ) is the bundle 8k space of the bundle associated with with fiber the unit ball D. There is also a linear isomorphism od 9 : R ev ( 5 ' ) | JD ...
... associated two real vector space bundles Rod ( ' ) and Rev ( ' ) over D ( 5 ) , where D ( 5 ) is the bundle 8k space of the bundle associated with with fiber the unit ball D. There is also a linear isomorphism od 9 : R ev ( 5 ' ) | JD ...
Page 30
... associated sphere bundle is given by E ( § ) × ( U ( n ) / U ( n − 1 ) ) / U ( n ) → X. There is an identification ... associated with is thus identified with the natural map E ( ) / U ( n - 1 ) →→→→ X. If is taken to be a ...
... associated sphere bundle is given by E ( § ) × ( U ( n ) / U ( n − 1 ) ) / U ( n ) → X. There is an identification ... associated with is thus identified with the natural map E ( ) / U ( n - 1 ) →→→→ X. If is taken to be a ...
Page 98
... associated map . Denote by T T ( k ) the Thom class in à ( MU ( k ) ) , let be the orientation class of s2n + 2k and consider Then 8 : a * f * H2n + 2k ( s2n + 2k ) H2n + 2k ( MU ( k ) / s2k ) H ( MU ( n ) ) . 2n + 2k Proof . Td [ M2n ] ...
... associated map . Denote by T T ( k ) the Thom class in à ( MU ( k ) ) , let be the orientation class of s2n + 2k and consider Then 8 : a * f * H2n + 2k ( s2n + 2k ) H2n + 2k ( MU ( k ) / s2k ) H ( MU ( n ) ) . 2n + 2k Proof . Td [ M2n ] ...
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