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

• Autorzy: Peter Wong
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

fixed points; coincidences; roots; Lefschetz number; Nielsen number

Kategorie tematyczne

• 55M20: Fixed points and coincidences

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1991-1992
• Tom: 140
• Numer: 2
• Strony: 191-196

Daty

wydano

1992

otrzymano

1991-07-24

poprawiono

1991-10-08

Twórcy

autor

Peter Wong

• Department of Mathematics, Bates College Lewiston, Maine 04240, U.S.A.

Bibliografia

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