The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 42
... prove the theorem of Dolá [ 12 ] . ( 7.4 ) DOLD . Suppose that 77 : EX is a locally trivial fibering with fiber F , where X and F are finite CW complexes . n n Suppose that C1 ɛ h ( E ) are such that for each x 。& X the h - module h ...
... prove the theorem of Dolá [ 12 ] . ( 7.4 ) DOLD . Suppose that 77 : EX is a locally trivial fibering with fiber F , where X and F are finite CW complexes . n n Suppose that C1 ɛ h ( E ) are such that for each x 。& X the h - module h ...
Page 55
... prove the theorem , it suffices to prove also multiplicative . = that 24 : ( HP ( n ) ) →→→ K0 * ( HP ( n ) ) Sp image of PA Pn maps the P of ( 8.1 ) into the element of ( 9.1 ) . ≈ Let p'n denote the 04 in Q Sp SU and it suffices ...
... prove the theorem , it suffices to prove also multiplicative . = that 24 : ( HP ( n ) ) →→→ K0 * ( HP ( n ) ) Sp image of PA Pn maps the P of ( 8.1 ) into the element of ( 9.1 ) . ≈ Let p'n denote the 04 in Q Sp SU and it suffices ...
Page 66
... 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 divisor in call some facts [ 2 ] . There is a boundary operator a : nu → Qu taking [ wn ] into [ v2n - 2 ] ...
... 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 divisor in call some facts [ 2 ] . There is a boundary operator a : nu → Qu taking [ wn ] into [ v2n - 2 ] ...
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