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

100%

Wong P.

Fundamenta Mathematicae

1991-1992

tom 140

nr 2

191-196

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.

Corrections to "On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem" (Fund. Math. 140 (1992), 191–196)

100%

Wong P.

Fundamenta Mathematicae

1992

tom 141

nr 1

97-99

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Wong P.

2 1992

Wyniki wyszukiwania

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

Corrections to "On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem" (Fund. Math. 140 (1992), 191–196)