The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 66
... polynomial algebra each dimension 8k . 2 over Z2 with generators in SU Also all torsion of U is of the form [ w8m ] [ 51 ] or [ W [ w8m ] [ 5 ] [ 5 ] where [ w ] & SU represents a non - zero element of SU 8m ε Ω Im / Im . Finally if ...
... polynomial algebra each dimension 8k . 2 over Z2 with generators in SU Also all torsion of U is of the form [ w8m ] [ 51 ] or [ W [ w8m ] [ 5 ] [ 5 ] where [ w ] & SU represents a non - zero element of SU 8m ε Ω Im / Im . Finally if ...
Page 78
... polynomial of x . Letting Ck = c ( x ) , it is the famous polynomial 2 ( Tx ) -1 = 1 + + C1 + 12 C2 + 2 + C1C2 + 3 + · 24 ° 13 of Hirzebruch [ 16 ] . Suppose now that Mn is a U - manifold . - The stable tangent bundle T + ( 2k ...
... polynomial of x . Letting Ck = c ( x ) , it is the famous polynomial 2 ( Tx ) -1 = 1 + + C1 + 12 C2 + 2 + C1C2 + 3 + · 24 ° 13 of Hirzebruch [ 16 ] . Suppose now that Mn is a U - manifold . - The stable tangent bundle T + ( 2k ...
Page 85
... polynomial 9 a symmetric polynomial * ** mod p for x , y symmetric . * • Note that Adding this to the previous ( xy ) = x y fact that x [ M ] = 0 unless w = 0 or w = ( xy • • • w ) [ M ] = ( p * , ... , pk ) p ) we get ( xy ••• w ) [ M ] ...
... polynomial 9 a symmetric polynomial * ** mod p for x , y symmetric . * • Note that Adding this to the previous ( xy ) = x y fact that x [ M ] = 0 unless w = 0 or w = ( xy • • • w ) [ M ] = ( p * , ... , pk ) p ) we get ( xy ••• w ) [ M ] ...
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