Nielsen coincidence theory and coincidence-producing maps for manifolds with boundary

Abstract

Nielsen coincidence theory is extended to manifolds with boundary. For X and Y compact connected oriented n-manifolds with boundary, and for maps ƒ : X → Y and g : ( X, ∂ X) → ( Y, ∂ Y), a coincidence index—which is a local version of Nakaoka's Lefschetz coincidence number—and a Nielsen coincidence number are defined and their properties explored. As an application, coincidence-producing maps g are characterized if Y is acyclic over the rationals and many new examples of coincidence-producing maps are constructed.