The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
From inside the book
Results 1-5 of 41
Page 4
... Consider the complex inner product space V of dimension n , with given SU - structure . If n = 4k + 2 then AV becomes a right quaternionic vector space by defining Y⚫j = ( Y ) for Y & ɅV . Moreover SU ( n ) acts on AV in a quaternionic ...
... Consider the complex inner product space V of dimension n , with given SU - structure . If n = 4k + 2 then AV becomes a right quaternionic vector space by defining Y⚫j = ( Y ) for Y & ɅV . Moreover SU ( n ) acts on AV in a quaternionic ...
Page 5
... consider AV as a Z - graded quaternionic vector space while if m = 0 mod 4 we obtain a Z - graded real vector space RV . A main purpose of this section is to prove the following . ( 2.1 ) THEOREM . There exist natural isomorphisms R ( V ...
... consider AV as a Z - graded quaternionic vector space while if m = 0 mod 4 we obtain a Z - graded real vector space RV . A main purpose of this section is to prove the following . ( 2.1 ) THEOREM . There exist natural isomorphisms R ( V ...
Page 6
... consider now the proof of ( 2.1 ) for m = 4k and n = 41 . There is a natural homomorphism Y : AV 1W → AV R ^ W γ : ο AW R - C whose kernel is generated by all Xi Y x Yi . On the real tensor product there is the involution 12 , and ...
... consider now the proof of ( 2.1 ) for m = 4k and n = 41 . There is a natural homomorphism Y : AV 1W → AV R ^ W γ : ο AW R - C whose kernel is generated by all Xi Y x Yi . On the real tensor product there is the involution 12 , and ...
Page 7
... Consider then R RV RW AV AW → A ( V + W ) R C which by ( 2.1 ) has image in R ( V + W ) . It is seen that if y ɛ Kernel , then ( 1 i ) y = - ( 11 ) y . If also y & R ( V ) ✪ R ( W ) then the left hand side belongs to ® R ✪ ® R_ ( V ) ...
... Consider then R RV RW AV AW → A ( V + W ) R C which by ( 2.1 ) has image in R ( V + W ) . It is seen that if y ɛ Kernel , then ( 1 i ) y = - ( 11 ) y . If also y & R ( V ) ✪ R ( W ) then the left hand side belongs to ® R ✪ ® R_ ( V ) ...
Page 8
... consider v + w ɛ V + W. Using the identification Ʌ ( v + W ) : = AV✪ AW , we have 9т ( XY ) = 9 XO Y + ( -1 ) * x® 9 1 , X € X € Akv . Hence V + W V W Proof . The element vw corresponds to v 1 + 1 w ε ^ V ^ W . where f : Fy + w ( X® Y ) ...
... consider v + w ɛ V + W. Using the identification Ʌ ( v + W ) : = AV✪ AW , we have 9т ( XY ) = 9 XO Y + ( -1 ) * x® 9 1 , X € X € Akv . Hence V + W V W Proof . The element vw corresponds to v 1 + 1 w ε ^ V ^ W . where f : Fy + w ( X® Y ) ...
Other editions - View all
Common terms and phrases
abelian group algebra base point bordism bordism classes BSp(n bundle map c₁ ch+k characteristic classes Chern classes Chern numbers closed U-manifold cobordism coefficient groups cohomology theory complex inner product complex vector space consider COROLLARY CP(n CW pair X,A define denote diagram dimension Dold element epimorphism ɛ K(M finite CW complex finite CW pair framed manifold Hence Hirzebruch homotopy class Hopf HP(n identified induced inner product space integer K-theory kernel KSP(X LEMMA line bundle M²n map f module monomial MSU 4k MU(k multiplicative cohomology theory n+2k 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 unitary vector space bundle Z-graded εΩ Ωυ हु