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Fibrations and homology sphere bordism. (English) Zbl 0795.55006

We discuss the homology sphere bordism groups, \(\Omega_ *^{HS} (-)\), of J.-C. Hausmann [see e.g. J.-C. Hausmann and P. Vogel, The plus construction and lifting maps from manifolds, Algebr. geom. Topol., Stanford/Calif. 1976, Proc. Symp. pure Math., Vol. 32, Part 1, 67-76 (1978; Zbl 0409.57036)], with special emphasis on the properties of these groups in relation to fibrations. The interest in these groups derives from a strong relation to algebraic K-theory, and as a good realization of what P. Vogel called the homological Hurewicz theorem. The main point demonstrated here, is that these groups are quite accessible from ordinary obstruction theory, and that, if the action of a particular part of the fundamental group is not too wild, they behave quite well.
Reviewer: B.I.Dundas (Oslo)

MSC:

55N22 Bordism and cobordism theories and formal group laws in algebraic topology

Citations:

Zbl 0409.57036
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