The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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... compact ( U , fr ) -manifolds M , where roughly a ( U , fr ) -manifold ... manifold M with a given complex structure on its stable tangent bundle T and a given compatible framing of restricted to the boundary M. These bordism classes have ...
... compact ( U , fr ) -manifolds M , where roughly a ( U , fr ) -manifold ... manifold M with a given complex structure on its stable tangent bundle T and a given compatible framing of restricted to the boundary M. These bordism classes have ...
Page 69
... if and only if Ta [ m2 ] is an integer . In section 16 we consider bordism classes of compact ( U , fr ) -mani- folds M1 ; these may be identified with elements of the homotopy group ᅲ n + 2k ( MU ( k ) / 69 U-Manifolds with Framed ...
... if and only if Ta [ m2 ] is an integer . In section 16 we consider bordism classes of compact ( U , fr ) -mani- folds M1 ; these may be identified with elements of the homotopy group ᅲ n + 2k ( MU ( k ) / 69 U-Manifolds with Framed ...
Page 93
... compact U - manifold wn + 1 with with own + 1 = M " . The point of the remainder of this chapter is to consider such pairs ( wh + 1 , мn ) . A ( U , fr ) -manifold ... U - manifold N having the same Chern 93.
... compact U - manifold wn + 1 with with own + 1 = M " . The point of the remainder of this chapter is to consider such pairs ( wh + 1 , мn ) . A ( U , fr ) -manifold ... U - manifold N having the same Chern 93.
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