The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 66
... bordism . SU Denote by the bordism ring of closed SU - manifolds ( denoted by in [ 12 ] ) . We 8n must prove that if [ Mon ) e ( ) SU 8n * has Todd genus T [ M8n ] + = 1 , then 8n SU In order to prove this we re- [ M ] is not a zero ...
... bordism . SU Denote by the bordism ring of closed SU - manifolds ( denoted by in [ 12 ] ) . We 8n must prove that if [ Mon ) e ( ) SU 8n * has Todd genus T [ M8n ] + = 1 , then 8n SU In order to prove this we re- [ M ] is not a zero ...
Page 69
... bordism and K - theory . In section 12 we consider the bordism group of ( U n Ωυ U of closed U - manifolds of dimension n ; the elements n are the bordism classes [ M ] of closed differentiable manifolds with a given complex structure ...
... bordism and K - theory . In section 12 we consider the bordism group of ( U n Ωυ U of closed U - manifolds of dimension n ; the elements n are the bordism classes [ M ] of closed differentiable manifolds with a given complex structure ...
Page 72
... bordism relation on closed U - manifolds by 1 2 M ~ M if there exists a compact U - manifold wh + 1 with own + l the disjoint union ( M2 ) M1 ~ One as U - manifolds . This is an equivalence relation ; denote the bordism class containing ...
... bordism relation on closed U - manifolds by 1 2 M ~ M if there exists a compact U - manifold wh + 1 with own + l the disjoint union ( M2 ) M1 ~ One as U - manifolds . This is an equivalence relation ; denote the bordism class containing ...
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