Related papers: Nielsen equalizer theory
Given two maps between smooth manifolds, the obstruction to removing their coincidences (via homotopies) is measured by minimum numbers. In order to determine them we introduce and study an infinite hierarchy of Nielsen numbers N_i, i = 0,…
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…
Minimum numbers measure the obstruction to removing coincidences of two given maps (between smooth manifolds M and N of dimensions m and n, resp.). In this paper we compare them to four distinct types of Nielsen numbers. These agree with…
In classical fixed point and coincidence theory the notion of Nielsen numbers has proved to be extremely fruitful. Here we extend it to pairs (f_1, f_2) of maps between manifolds of arbitrary dimensions. This leads to estimates of the…
Given two maps f_1, f_2 : M^m \longrightarrow N^n between manifolds of the indicated arbitrary dimensions, when can they be deformed away from one another? More generally: what is the minimum number MCC (f_1, f_2) of pathcomponents of the…
In classical fixed point and coincidence theory the notion of Nielsen numbers has proved to be extremely fruitful. We extend it to pairs (f_1,f_2) of maps between manifolds of arbitrary dimensions, using nonstabilized normal bordism theory…
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…
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…
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…
Suppose X,Y are manifolds, f,g:X->Y are maps. The well-known Coincidence Problem studies the coincidence set C={x:f(x)=g(x)}. The number m=dimX-dimY is called the codimension of the problem. More general is the Preimage Problem. For a map…
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)…
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…
In this article we studied Nielsen coincidence theory for maps between manifolds of same dimension without hypotheses on orientation. We use the definition of semi-index of a class, we review the definition of defective classes and study…
We derive a formula for the Nielsen number $N(f)$ for every $n$-valued self-map $f$ of an infra-solvmanifold. To do this, we express $N(f)$ in terms of Nielsen coincidence numbers of single-valued maps on solvmanifolds, and derive a formula…
The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidence index is an extension of the concept to…
We study the asymptotic behavior of the sequence of the Nielsen numbers $\{N(f^k)\}$, the essential periodic orbits of $f$ and the homotopy minimal periods of $f$ by using the Nielsen theory of maps $f$ on infra-solvmanifolds of type $R$.…
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…
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…
We consider the homotopical dynamics on compact orientable surfaces of positive genus g. We establish a sufficient and necessary algebraic criterion for homotopy classes with infinitely many periodic points of maps on such surfaces in terms…
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…