Necklace bisection with one cut less than needed.
Nielsen fixed point theory and symplectic Floer homology
We describe a connection between Nielsen fixed point theory and symplectic Floer homology for surfaces. A new asymptotic invariant of symplectic origin is defined.
Nielsen fixed point theory on manifolds
The study of fixed points of continuous self-maps of compact manifolds involves geometric topology in a significant way in topological fixed point theory. This survey will discuss some of the questions that have arisen in this study and indicate our present state of knowledge, and ignorance, of the answers to them. We will limit ourselves to the statement of facts, without any indication of proof. Thus the reader will have to consult the references to find out how geometric topology has contributed...
Nielsen number is a knot invariant
We show that the Nielsen number is a knot invariant via representation variety.
Nielsen number of a covering map.
Nielsen theory of transversal fixed point sets (with an appendix: and C0 fixed point sets are the same, by R. E. Greene)
Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of fixed points...
Nielsen type numbers of self-maps on the real projective plane.
Nielsen zeta function, 3-manifolds, and asymptotic expansions in Nielsen theory.