Geodesic
On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem
Fundamenta Mathematicae, Tome 140 (1991) no. 2, pp. 191-196

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Let $f,g:M_1 → M_2$ be maps where $M_1$ and $M_2$ are connected triangulable oriented n-manifolds so that the set of coincidences $C_{f,g}= {x ∈ M_1 | f(x)=g(x)}$ is compact in $M_1$. We define a Nielsen equivalence relation on $C_{f,g}$ and assign the coincidence index to each Nielsen coincidence class. In this note, we show that, for n ≥ 3, if $M_2= \widetilde M_2/K$ where $\widetilde M_2$ is a connected simply connected topological group and K is a discrete subgroup then all the Nielsen coincidence classes of f and g have the same coincidence index. In particular, when $M_1$ and $M_2$ are compact, f and g are deformable to be coincidence free if the Lefschetz coincidence number L(f,g) vanishes.
DOI : 10.4064/fm-140-2-191-196
Keywords: fixed points, coincidences, roots, Lefschetz number, Nielsen number

Peter Wong 1

1 
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Peter Wong. On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem. Fundamenta Mathematicae, Tome 140 (1991) no. 2, pp. 191-196. doi: 10.4064/fm-140-2-191-196

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