A Lefschetz trace formula for equivariant cohomology
A Lefschetz-type coincidence theorem for two maps f,g: X → Y from an arbitrary topological space to a manifold is given: , that is, the coincidence index is equal to the Lefschetz number. It follows that if then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y Euclidean, f with acyclic fibres. It also implies certain fixed point results for multivalued maps with “point-like” (acyclic)...
We prove an existence and multiplicity result for solutions of a nonlinear Urysohn type equation (2.14) by use of the Nielsen and degree theory in an annulus in the function space.