The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
From inside the book
Results 1-3 of 20
Page 3
... unique monomial X with X ( 1.1 ) If X is a monomial then X is the unique monomial X with X 1 x = σ This is readily seen from the definition of T. ( 1.2 ) We have 72x = ( -1 ) k ( n - k ) x for X ɛ * v . Proof . It is sufficient to prove ...
... unique monomial X with X ( 1.1 ) If X is a monomial then X is the unique monomial X with X 1 x = σ This is readily seen from the definition of T. ( 1.2 ) We have 72x = ( -1 ) k ( n - k ) x for X ɛ * v . Proof . It is sufficient to prove ...
Page 6
... unique monomial Ĩ with X ^ X = σ 1 the unique monomial Y with Y Y = σ Then · 2 ( X ^ X ) R ( Y ^ Ÿ ) = and ( −1 ) s ( m - r ) ( x® Y ) ^ ( X® Y ) ( XY ) ( -1 ) s ( m - r ) ~ 1x® ~ Y . Since = α ( X® Y ) = ( -1 ) rs xx® αy , then = σ Tα ...
... unique monomial Ĩ with X ^ X = σ 1 the unique monomial Y with Y Y = σ Then · 2 ( X ^ X ) R ( Y ^ Ÿ ) = and ( −1 ) s ( m - r ) ( x® Y ) ^ ( X® Y ) ( XY ) ( -1 ) s ( m - r ) ~ 1x® ~ Y . Since = α ( X® Y ) = ( -1 ) rs xx® αy , then = σ Tα ...
Page 26
... unique homotopy class of bundle maps 1 + 7 is an SU ( n + 1 ) -bundle , there is a そ n Zn + 1 , also It is M ( 1 + ... unique The unique class of bundle maps n k homotopy class of maps MSU ( k ) ^ MSU ( X ) →→→→ MSU ( k + X ) , and ...
... unique homotopy class of bundle maps 1 + 7 is an SU ( n + 1 ) -bundle , there is a そ n Zn + 1 , also It is M ( 1 + ... unique The unique class of bundle maps n k homotopy class of maps MSU ( k ) ^ MSU ( X ) →→→→ MSU ( k + X ) , and ...
Contents
The Thom Isomorphism in Ktheory | 1 |
Cobordism Characteristic Classes | 38 |
UManifolds with Framed Boundaries | 69 |
Copyright | |
1 other sections not shown
Other editions - View all
Common terms and phrases
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