Equivariant Nielsen numbers

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 ...

Equivariant Nielsen Invariants for Discrete Groups

For discrete groups G, we introduce equivariant Nielsen invariants. They are equivariant analogs of the Nielsen number and give lower bounds for the number of fixed point orbits in the G-homotopy class of an equivariant endomorphism f : X → X. Under mild hypotheses, these lower bounds are sharp. We use the equivariant Nielsen invariants to show that a G-equivariant endomorphism f is G-homotopic...

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)...

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...

Estimating Nielsen Numbers on Wedge Product Spaces