Related papers: Nielsen numbers of $n$-valued maps on infra-solvma…

In [8,9], the authors developed a nice formula to compute the Nielsen number of a self-map on an infra-nilmanifold. For the case of nilmanifolds this formula was extended to $n$-valued maps in [4]. In this paper, we extend these results…

Until now only for special classes of infra-solvmanifolds, namely infra-nilmanifolds and infra-solvmanifolds of type (R), there was a formula available for computing the Nielsen number of a self-map on those manifolds. In this paper, we…

For an $n$-valued self-map $f$ of a closed manifold $X$, we prove an averaging formula for the Reidemeister trace of $f$ in terms of the Reidemeister coincidence traces of single-valued maps between finite orientable covering spaces of $X$.…

We generalise Nielsen theory to coincidences of pairs $(f,g)$ where $f:X\multimap Y$ is $n$-valued multimap and $g:X\to Y$ is a single-valued map, for $X$ and $Y$ closed oriented triangulable manifolds of equal dimension. We prove a Wecken…

A nilmanifold is a quotient N\G of a connected and simply connected nilpotent Lie group G by a uniform lattice N. In this paper we determine the Reidemeister and Nielsen number of affine n-valued maps on such a nilmanifold. These are maps…

Let $f_1,...,f_k:M\to N$ be maps between closed manifolds, $N(f_1,...,f_k)$ and $R(f_1,...,f_k)$ be the Nielsen and the Reideimeister coincidence numbers respectively. In this note, we relate $R(f_1,...,f_k)$ with…

We discuss coincidences of pairs (f_1, f_2) of maps between manifolds. We recall briefly the definition of four types of Nielsen numbers which arise naturally from the geometry of generic coincidences. They are lower bounds for the minimum…

In this paper, we expand certain aspects of Nielsen periodic point theory from tori and nilmanifolds to infra-nilmanifolds. We show that infra-nilmanifolds are essentially reducible to the GCD and essentially toral. With these structural…

We show that the Nielsen number of a map is a knot invariant via representation variety

We consider pairs of maps $(f,g)$, where $f$ is an $n$-valued map and $g$ is an $m$-valued map, defined on connected finite polyhedra. A point $x$ such that $f(x)\cap g(x)\neq \emptyset$ is called a coincidence point of $f$ and $g$. A…

In this paper we study 2-valued non-split maps, focusing on the Klein bottle. We establish a connection between a 2-valued non-split map $\phi:X\multimap Y$ and a pair of classes of maps $([f],[f\circ \delta])\in [\tilde X,Y]\times[\tilde…

In [3,9], the Nielsen zeta function $N_f(z)$ has been shown to be rational if $f$ is a self-map of an infra-solvmanifold of type (R). It is, however, still unknown whether $N_f(z)$ is rational for self-maps on solvmanifolds. In this paper,…

In this paper we continue to study (`strong') Nielsen coincidence numbers (which were introduced recently for pairs of maps between manifolds of arbitrary dimensions) and the corresponding minimum numbers of coincidence points and…

We extend the Nielsen theory of coincidence sets to equalizer sets, the points where a given set of (more than 2) mappings agree. On manifolds, this theory is interesting only for maps between spaces of different dimension, and our results…

Let M to B, N to B be fibrations and f1,f2 :M to N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f1,f2 over B to a coincidence free pair of maps.In…

As the title suggests, this paper gives a Nielsen theory of coincidences of iterates of two self maps f, g of a closed manifold. The ideas is, as much as possible, to generalize Nielsen type periodic point theory, but there are many…

Given two maps f1 and f2 from the sphere Sm to an n-manifold N, when are they loose, i.e. when can they be deformed away from one another? We study the geometry of their (generic) coincidence locus and its Nielsen decomposition. On the one…

Given two fiberwise maps f1, f2 between smooth fiber bundles over a base manifold B, we develop techniques for calculating their Nielsen coincidence number. In certain settings we can describe the Reidemeister set of (f1,f2) as the orbit…

Let $Y \to E \stackrel{p}{\to} B$ be a fibration and let $f: E \to E$ be a fiber map over $B$. In this work, we study the geometric and algebraic Reidemeister classes of the iterates of $f$ and introduce a Nielsen-type periodic number over…

Let $ f_1, f_2 \colon X^m \longrightarrow Y^n $ be maps between smooth connected manifolds of the indicated dimensions $ \!m\! $ and $ \!n \!\!\!$. Can $ f_1, f_2 $ be deformed by homotopies until they are coincidence free (i.e. $ f_1(x)…