@article{Bogatyi2008OnMO,
title={On multiplicity of mappings between surfaces},
author={S. Bogatyi and J. Fricke and E. Kudryavtseva},
journal={arXiv: Geometric Topology},
year={2008}
}

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… CONTINUE READING