On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem

Wong, Peter

Wong, Peter

Fundamenta Mathematicae, Tome 141 (1992), p. 191-196 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $f, g : M_{1} \to M_{2}$ be maps where $M_{1}$ and $M_{2}$ are connected triangulable oriented n-manifolds so that the set of coincidences $C_{f, g} = x \in M_{1} | f (x) = g (x)$ 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 $M_{2} = {\tilde{M}}_{2} / K$ where ${\tilde{M}}_{2}$ 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.

Publié le : 1992-01-01

Zbl 0809.55001

EUDML-ID : urn:eudml:doc:211938

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     author = {Peter Wong},
     title = {On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem},
     journal = {Fundamenta Mathematicae},
     volume = {141},
     year = {1992},
     pages = {191-196},
     zbl = {0809.55001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv140i2p191bwm}
}

Wong, Peter. On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem. Fundamenta Mathematicae, Tome 141 (1992) pp. 191-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv140i2p191bwm/

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