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References (18)
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A LOWER BOUND FOR THE A-NIELSEN NUMBER -
D. Gonçalves (1998)
Coincidence Reidemeister classes on nilmanifolds and nilpotent fibrationsTopology and its Applications, 83
- Publisher
- de Gruyter
- Copyright
- Copyright © 2001 by Walter de Gruyter GmbH & Co. KG
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- DOI
- 10.1515/form.2001.002
- Publisher site
- See Article on Publisher Site
Abstract
Abstract. Let MY N be closed orientable n-manifolds. If N is a nilmanifold, then we show that for any maps f Y g X M 3 N, all coincidence classes of f and g are either all essential or all inessential so that L f Y g 0 A N f Y g 0 or L f Y g H 0 A N f Y g R f Y g where L f Y g, N f Y g and R f Y g denote the Lefschetz, Nielsen and Reidemeister coincidence numbers of f and g, respectively. In particular, the converse of the Lefschetz coincidence theorem holds, i.e., L f Y g 0 implies that f and g can be deformed to be coincidence free. Similar results when M is not a manifold or a manifold of dimension greater than n are also given. 1991 Mathematics Subject Classi®cation: 55M20; 57T15. 1 Introduction The converse of the Lefschetz-Hopf ®xed point theorem does not hold in general, i.e., the vanishing of the Lefschetz number L f is not su½cient to deform a selfmap f X X 3 X on a compact polyhedron X to be ®xed point free. The Nielsen
Journal
Forum Mathematicum – de Gruyter
Published: Jan 5, 2001