Modules de SU-bordisme. Applications. (SU-bordism modules. Applications). (French) Zbl 0641.57015
In two previous papers, the author made a study of the homological properties of the SU-bordism functor. This extended the ideas of Conner and Smith on the U-bordism functor. This paper applies the homological theory of SU-bordism to two problems. First, the author shows that the Conner-Floyd map \(\Omega_*^{SU}(X)\times KO_*(pt)\to KO_*(X)\) is not an isomorphism, but that after multipliying by the generator of \(\Omega_ 1^{SU}\) one obtains an isomorphism. The second application is a study of regular sequences for coherent exact couples of SU-bordism modules. In particular, coherent exact couples of given homological dimension are constructed.
Reviewer: R.E.Stong
MSC:
| 57R77 | Complex cobordism (\(\mathrm{U}\)- and \(\mathrm{SU}\)-cobordism) |
| 55N15 | Topological \(K\)-theory |
| 55N22 | Bordism and cobordism theories and formal group laws in algebraic topology |
Keywords:
SU-bordism functor; Conner-Floyd map; regular sequences for coherent exact couples of SU-bordism modules; homological dimensionReferences:
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