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

Peter Wong — 1992

Fundamenta Mathematicae

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...

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

Peter Wong — 1992

Fundamenta Mathematicae

Equivariant Nielsen theory

Peter Wong — 1999

Banach Center Publications

Fixed point theory for homogeneous spaces, II

Peter Wong — 2005

Fundamenta Mathematicae

Let G be a compact connected Lie group, K a closed subgroup and M = G/K the homogeneous space of right cosets. Suppose that M is orientable. We show that for any selfmap f: M → M, L(f) = 0 ⇒ N(f) = 0 and L(f) ≠ 0 ⇒ N(f) = R(f) where L(f), N(f), and R(f) denote the Lefschetz, Nielsen, and Reidemeister numbers of f, respectively. In particular, this implies that the Lefschetz number is a complete invariant, i.e., L(f) = 0 iff f is deformable to be fixed point free. This was previously known under...

Equivariant evaluation subgroups and Rhodes groups

Marek Golasiński; Daciberg Gonçalves; Peter Wong — 2007

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Coincidence theory for spaces which fiber over a nilmanifold.

Wong, Peter — 2004

Fixed Point Theory and Applications [electronic only]

A note on generalized equivariant homotopy groups

Marek Golasiński; Daciberg L. Gonçalves; Peter N. Wong — 2009

Banach Center Publications

In this paper, we generalize the equivariant homotopy groups or equivalently the Rhodes groups. We establish a short exact sequence relating the generalized Rhodes groups and the generalized Fox homotopy groups and we introduce Γ-Rhodes groups, where Γ admits a certain co-grouplike structure. Evaluation subgroups of Γ-Rhodes groups are discussed.

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Currently displaying 1 – 7 of 7

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)

Equivariant Nielsen theory

Fixed point theory for homogeneous spaces, II

Equivariant evaluation subgroups and Rhodes groups

Coincidence theory for spaces which fiber over a nilmanifold.

A note on generalized equivariant homotopy groups