%0 Journal Article
%T On multiplicity of mappings between surfaces
%A Semeon Bogatyi
%A Jan Fricke
%A Elena Kudryavtseva
%J Mathematics
%D 2009
%I arXiv
%R 10.2140/gtm.2008.14.49
%X Let M and N be two closed (not necessarily orientable) surfaces, and f a continuous map from M to N. By definition, the minimal multiplicity MMR[f] of the map f denotes the minimal integer k having the following property: f can be deformed into a map g such that the number |g^{-1}(c)| of preimages of any point c in N under g is at most k. We calculate MMR[f] for any map $f$ of positive absolute degree A(f). The answer is formulated in terms of A(f), [pi_1(N):f_#(pi_1(M))], and the Euler characteristics of M and N. For a map f with A(f)=0, we prove the inequalities 2 <= MMR[f] <= 4.
%U http://arxiv.org/abs/0904.1197v1