Estimating Nielsen numbers on infrasolvmanifolds

Estimating Nielsen Numbers on Infrasolvmanifolds

A well-known lower bound for the number of xed points of a self-map f : X ?! X is the Nielsen number N(f). Unfortunately, the Nielsen number is diicult to calculate. The Lefschetz number L(f), on the other hand, is readily computable, but does not give a lower bound for the number of xed points. In this paper, we investigate conditions on the space X which guarantee either N(f) = jL(f)j or N(f)...

Estimating Nielsen Numbers on Wedge Product Spaces

Higher-order Nielsen Numbers

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 f : X → Z and a submanifold Y of Z, it studies the preimage set C = {x : f (x) ∈ Y}, and the codimension is m = dimX + dimY − dimZ. In case of ...

Lefschetz and Nielsen Coincidence Numbers on Nilmanifolds and Solvmanifolds

Suppose M 1 ; M 2 are compact, connected orientable manifolds of the same dimension. Then for all pairs of maps f,g:M 1 ?! M 2 , the Nielsen coincidence number N(f,g) and the Lefschetz coincidence number L(f,g) are measures of the number of coincidences of f and g: points x 2 M 1 with f(x) = g(x). A manifold is a nilmanifold (solvmanifold) if it is a homogeneous space of a nilpotent (solvable) ...

NIELSEN NUMBERS OF n-VALUED FIBERMAPS

The Nielsen number for n-valued multimaps, defined by Schirmer, has been calculated only for the circle. A concept of n-valued fiber map on the total space of a fibration is introduced. A formula for the Nielsen numbers of n-valued fiber maps of fibrations over the circle reduces the calculation to the computation of Nielsen numbers of single-valued maps. If the fibration is orientable, the pro...