The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 4
... acts on AV by Identify the special unitary group gv , gk SU ( n ) with the set of all g ɛ U ( n ) for which g ( 0 ) = σ . ( 1.4 ) Proof . If g ε SU ( n ) , then g = Tg Tв and MB = вро From < ~ X , Y > = ( ~ , Xn Y > we get < g ~ X , gY > ...
... acts on AV by Identify the special unitary group gv , gk SU ( n ) with the set of all g ɛ U ( n ) for which g ( 0 ) = σ . ( 1.4 ) Proof . If g ε SU ( n ) , then g = Tg Tв and MB = вро From < ~ X , Y > = ( ~ , Xn Y > we get < g ~ X , gY > ...
Page 5
... acts on the quaternionic vector od ev spaces V and V. If n = 0 mod 4 then SU ( n ) acts on the real vector spaces R Rody and Revv . 2 . Tensor products of exterior algebras . Let V and W be complex inner product spaces of dimension and ...
... acts on the quaternionic vector od ev spaces V and V. If n = 0 mod 4 then SU ( n ) acts on the real vector spaces R Rody and Revv . 2 . Tensor products of exterior algebras . Let V and W be complex inner product spaces of dimension and ...
Page 11
... acts on the left on AV and there is the complex vector space bundle ( ) → X , where ( ( ( 5 ) = E ( 5 ) × E ( 3 ) × ɅV / SU ( n ) and where SU ( n ) acts on the right on E ( ) x AV by ( e , Y ) g = The orbit of ( e , Y ) under this ...
... acts on the left on AV and there is the complex vector space bundle ( ) → X , where ( ( ( 5 ) = E ( 5 ) × E ( 3 ) × ɅV / SU ( n ) and where SU ( n ) acts on the right on E ( ) x AV by ( e , Y ) g = The orbit of ( e , Y ) under this ...
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