Abstract

Let G be a compact connected Lie group, K a closed subgroup (not necessarily connected) and M = G/K the homogeneous space of left cosets. Assume that M is orientable and p*: Hn(G) → Hn(M) is nonzero, where n = dim M. In this paper, we employ an equivariant version of Nielsen root theory to show that the converse of the Lefschetz fixed-point theorem holds true for all selfmaps on M. Moreover, if the Lefschetz number of a selfmap f : MM is nonzero, then the Nielsen number of f coincides with the Reidemeister number of f, which can be computed algebraically.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 23-42
Launched on MUSE
1998-02-01
Open Access
No
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