The Relation of Cobordism to K-TheoriesSpringer, 2006 M11 14 - 116 pages |
From inside the book
Results 1-5 of 12
Page
... Chapter I we treat the Thom isomorphism in K - theory . The families U , SU , Sp of unitary , special unitary , symplectic groups generate spectra MU , MSU , MSp of Thom spaces . In the fashion of G. W. Whitehead [ 26 ] , each spectrum ...
... Chapter I we treat the Thom isomorphism in K - theory . The families U , SU , Sp of unitary , special unitary , symplectic groups generate spectra MU , MSU , MSp of Thom spaces . In the fashion of G. W. Whitehead [ 26 ] , each spectrum ...
Page
... Chapter II we show among other things that the cobordism theories determine the K - theories . ring homomorphism shown that For example , generates a с * * → Z and makes Z into a module . It is U U * Kˆ ( X , A ) ≈ Qˆ ( X , A ) ® U N ...
... Chapter II we show among other things that the cobordism theories determine the K - theories . ring homomorphism shown that For example , generates a с * * → Z and makes Z into a module . It is U U * Kˆ ( X , A ) ≈ Qˆ ( X , A ) ® U N ...
Page
... Chapter III is in large part independent of Chapter II . It is to be noted that we have omitted spin cobordism completely ; this is because of our ignorance . However the recent work of Anderson- Brown - Peterson is a notable example of ...
... Chapter III is in large part independent of Chapter II . It is to be noted that we have omitted spin cobordism completely ; this is because of our ignorance . However the recent work of Anderson- Brown - Peterson is a notable example of ...
Page
... Chapter II . Cobordism Characteristic Classes 7. A theorem of Dold 8. Characteristic classes in cobordism 9. Characteristic classes in K - theory 10. A cobordism interpretation for K * ( X ) 1 1 5 11 18 • 25 • 30 38 39 48 52 59 11 ...
... Chapter II . Cobordism Characteristic Classes 7. A theorem of Dold 8. Characteristic classes in cobordism 9. Characteristic classes in K - theory 10. A cobordism interpretation for K * ( X ) 1 1 5 11 18 • 25 • 30 38 39 48 52 59 11 ...
Page 1
... chapter ; the methods have been well - known since the work of Atiyah - Hirzebruch [ 6 ] , Dold [ 13 ] , and others [ 7 ] . However since the results are needed explicitly in the later chapters we include an exposition . A deviation ...
... chapter ; the methods have been well - known since the work of Atiyah - Hirzebruch [ 6 ] , Dold [ 13 ] , and others [ 7 ] . However since the results are needed explicitly in the later chapters we include an exposition . A deviation ...
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