The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 59
... integer . Since 2n + 1 U = 0 ( see Milnor [ 19 ] ) , we thus have a ring homomorphism Q * → 2. Hence we can regard Z as a left U Mc : defining wa for we and a e Z to be the integer Ω U For ( X , A ) a finite pair define 1 * ( X , A ) ...
... integer . Since 2n + 1 U = 0 ( see Milnor [ 19 ] ) , we thus have a ring homomorphism Q * → 2. Hence we can regard Z as a left U Mc : defining wa for we and a e Z to be the integer Ω U For ( X , A ) a finite pair define 1 * ( X , A ) ...
Page 90
... integer сух [ m2 ] where the r's are rational Στ11 X © j1 © jp ••• varies over all partitions of n . Given integers > ... ≥ jx one for each partition of n , let a = aj1 , ... , jy ' ( aj1 ,, Jx : j 1 J. = n ) and let X sw ( a ) = Ex11 ...
... integer сух [ m2 ] where the r's are rational Στ11 X © j1 © jp ••• varies over all partitions of n . Given integers > ... ≥ jx one for each partition of n , let a = aj1 , ... , jy ' ( aj1 ,, Jx : j 1 J. = n ) and let X sw ( a ) = Ex11 ...
Page 96
... integer for W > 0. But s w ( a ) = sw [ M ] , hence ( a ) is an integer for > 0. But s̟ 。( a ) = Td [ м21 ] , which by assumption is an integer . The theorem now follows from ( 14.4 ) . 16. The bordism groups ( U , fr * Suppose that мn ...
... integer for W > 0. But s w ( a ) = sw [ M ] , hence ( a ) is an integer for > 0. But s̟ 。( a ) = Td [ м21 ] , which by assumption is an integer . The theorem now follows from ( 14.4 ) . 16. The bordism groups ( U , fr * Suppose that мn ...
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