Coincidence of maps from connected sums of closed surfaces into graphs

Roots of maps between spheres and projective spaces in codimension one

“…Proof. Let f : X → RP 2 be a map which is not null-homotopic, where X is either S 3 or RP 3 . By the proof of Lemma 5.1, f lifts through p 2 to a map f : X → S 2 which, obviously, is not null-homotopic.…”

“…In a context in which the involved spaces are not necessarily manifolds, the main theorem of [3] presents a necessary and sufficient condition for a pair of maps from a finite and connected 2-dimensional CW complex into a graph can be deformed to be coincidence free. The condition is given in terms of the existence of a lifting in a certain diagram of fundamental groups and induced homomorphisms.…”