The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 3
... seen that ^ e1 exx where r1 < ... < TM k • element X = erl if X and Y are monomials , then 1 if Y = X < X , Y > = -1 if Y = -X U otherwise . ^ X = σ . Moreover given a monomial X there is a unique monomial X with X ( 1.1 ) If X is a ...
... seen that ^ e1 exx where r1 < ... < TM k • element X = erl if X and Y are monomials , then 1 if Y = X < X , Y > = -1 if Y = -X U otherwise . ^ X = σ . Moreover given a monomial X there is a unique monomial X with X ( 1.1 ) If X is a ...
Page 7
... seen to have the same dimension , then Since RV RW R ( V + W ) . R It is also seen that the actions of SU ( m ) × SU ( n ) on the two sides are identified . RV If m = 4k and n = 47+ 2 then one sets up similarly an isomorphism AW ...
... seen to have the same dimension , then Since RV RW R ( V + W ) . R It is also seen that the actions of SU ( m ) × SU ( n ) on the two sides are identified . RV If m = 4k and n = 47+ 2 then one sets up similarly an isomorphism AW ...
Page 59
... seen that 1 * ( X , A ) ≈ ( 2 * ( X , A ) / R ( X , A ) U where R ( X , A ) is the least subgroup of ( * ( X , A ) generated by all cow - coμ ( w ) for c & ( * ( X , A ) and wɛ N * . U U U It is seen that 1 * ( • ) has many properties ...
... seen that 1 * ( X , A ) ≈ ( 2 * ( X , A ) / R ( X , A ) U where R ( X , A ) is the least subgroup of ( * ( X , A ) generated by all cow - coμ ( w ) for c & ( * ( X , A ) and wɛ N * . U U U It is seen that 1 * ( • ) has many properties ...
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