Strong surjectivity of maps from 2-complexes into the 2-sphere : Open Mathematics

摘要

Given a model 2-complex K P of a group presentation P, we associate to it an integer matrix ΔP and we prove that a cellular map f: K P → S 2 is root free (is not strongly surjective) if and only if the diophantine linear system ΔP Y = $$overrightarrow {deg} $$(f) has an integer solution, here $$overrightarrow {deg} $$(f)is the so-called vector-degree of f.