%0 Journal Article
%T Stable maps and branched shadows of 3-manifolds
%A Masaharu Ishikawa
%A Yuya Koda
%J Mathematics
%D 2014
%I arXiv
%X Turaev's shadow can be seen locally as the Stein factorization of a stable map. In this paper, we define the notion of stable map complexity for a compact orientable 3-manifold bounded by (possibly empty) tori counting, with some weights, the minimal number of singular fibers of codimension 2 of stable maps into the real plane, and prove that this number equals the minimal number of vertices of its branched shadows. In consequence, we give a complete characterization of hyperbolic links in the 3-sphere whose exteriors have stable map complexity 1 in terms of Dehn surgeries, and also give an observation concerning the coincidence of the stable map complexity and shadow complexity using estimations of hyperbolic volumes.
%U http://arxiv.org/abs/1403.0596v1