The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
From inside the book
Results 1-3 of 46
Page 19
... denote its < points by ( 1 tje + th where u ≤ t≤ 1 , e ɛ E ( ) , hɛ Sp ( 1 ) . Then - a principal action of Sp ( 1 ) is given by - ( ( 1 t ) eth ) g - = ( 1 − t ) eg + t'hg . ( 4.1 ) The Thom space M ( ) is canonically isomorphic to ...
... denote its < points by ( 1 tje + th where u ≤ t≤ 1 , e ɛ E ( ) , hɛ Sp ( 1 ) . Then - a principal action of Sp ( 1 ) is given by - ( ( 1 t ) eth ) g - = ( 1 − t ) eg + t'hg . ( 4.1 ) The Thom space M ( ) is canonically isomorphic to ...
Page 26
... denote by ( X ; M ) = Dir Lim [ sk ^ X , Mo + kd . n It is easily checked that H ( ; M ) is a cohomology theory . Note that it is sufficient to have only M2 , ·· , Man ' s2 ^ Mon M2n + 2 ' For one then defines g , • • • H " ( X ; M ) ...
... denote by ( X ; M ) = Dir Lim [ sk ^ X , Mo + kd . n It is easily checked that H ( ; M ) is a cohomology theory . Note that it is sufficient to have only M2 , ·· , Man ' s2 ^ Mon M2n + 2 ' For one then defines g , • • • H " ( X ; M ) ...
Page 75
... denoted simply by s ω ~ ( M2 ) = Σ γ . rx ( Mn ) tk ; k O As an example consider the U - manifold CP ( n ) . conjugate of the Hopf bundle over Cr ( n ) . Then ~ + 1 = ( n + 1 ) 5 ; more generally there is ) for any . Denote by the X ...
... denoted simply by s ω ~ ( M2 ) = Σ γ . rx ( Mn ) tk ; k O As an example consider the U - manifold CP ( n ) . conjugate of the Hopf bundle over Cr ( n ) . Then ~ + 1 = ( n + 1 ) 5 ; more generally there is ) for any . Denote by the X ...
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