The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 22
... base point , and of base point preserving maps . Denote by the category of Z - graded abelian groups and degree preserving homomorphisms . A G , assigning cohomology theory on is a contravariant functor → G , to each X a group ( x ) ...
... base point , and of base point preserving maps . Denote by the category of Z - graded abelian groups and degree preserving homomorphisms . A G , assigning cohomology theory on is a contravariant functor → G , to each X a group ( x ) ...
Page 25
... base point , together with base point preserving s1 1 maps ~ Mn →→ Mn + 1 • Given a finite CW complex X with base point , denote by [ X , maps X → M n 25 Cobordism and homomorphisms into K-theory.
... base point , together with base point preserving s1 1 maps ~ Mn →→ Mn + 1 • Given a finite CW complex X with base point , denote by [ X , maps X → M n 25 Cobordism and homomorphisms into K-theory.
Page 67
... basis ε 8n ( s8n ) . According * ( s8n ) is a free SU SU 8n SU where 8n to the first of this section , Po ( en ) = ß3_sn -8n ε -8n SU has ... base point such that * ( X ) is a free SU * -module . In the diagram SU ( x ) ΚΟ S j ñ3 ( x ) 67.
... basis ε 8n ( s8n ) . According * ( s8n ) is a free SU SU 8n SU where 8n to the first of this section , Po ( en ) = ß3_sn -8n ε -8n SU has ... base point such that * ( X ) is a free SU * -module . In the diagram SU ( x ) ΚΟ S j ñ3 ( x ) 67.
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