The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 15
... abelian . It is not difficult to show the existence of negatives , so that the set of equivalence classes becomes an abelian group . For fix nx ( 50 , 51 , 9 ) ; given a positive integer n denote by n the trivial bundle of dimension n ...
... abelian . It is not difficult to show the existence of negatives , so that the set of equivalence classes becomes an abelian group . For fix nx ( 50 , 51 , 9 ) ; given a positive integer n denote by n the trivial bundle of dimension n ...
Page 89
... abelian group Hom ( , Z ) of rank π ( n ) and 2n let KC Hom ( √ ) U , Z ) = G 2n be the subgroup spanned by all the swas w varies over all partitions En . with d ( w ) ≤ n . Now G / K is clearly a finite abelian group . Hence 18 there ...
... abelian group Hom ( , Z ) of rank π ( n ) and 2n let KC Hom ( √ ) U , Z ) = G 2n be the subgroup spanned by all the swas w varies over all partitions En . with d ( w ) ≤ n . Now G / K is clearly a finite abelian group . Hence 18 there ...
Page 92
... abelian group of bordism classes by fr . The cartesian product of two stably framed mani- folds is stably framed and fr ΣΩfr is a graded ring under n cartesian product [ 12 ] . = n n The abelian group fr is known to be isomorphic to the ...
... abelian group of bordism classes by fr . The cartesian product of two stably framed mani- folds is stably framed and fr ΣΩfr is a graded ring under n cartesian product [ 12 ] . = n n The abelian group fr is known to be isomorphic to the ...
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