buondì,

domani alle 16 c'è il consueto seminario di geometria, siete ovviamente tutti invitati. Bruno

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MERCOLEDI' 12 FEBBRAIO 2014

SEMINARI DI GEOMETRIA 16:00-17:00, Sala Seminari (Dip. Matematica) Branched shadows and stable maps Yuya Koda (Tohoku University, Universita` di Pisa)

Abstract: In the early 1990s, Turaev introduced the notion of shadows as a combinatorial presentation of both 4 and 3-manifolds. Later, Costantino-Thurston revealed a strong relation between the Stein factorizations of stable maps of 3-manifolds into the real plane and the shadows of the manifolds. In fact, a shadow can be seen locally as the Stein factorization of a stable map. In this talk, we define the notion of stable map complexity for a closed orientable 3-manifold counting, with some weights, the minimal number of codimension 2 singular fibers of stable maps into the real plane. Then we show that this number equals the minimal number of vertices of its branched shadows. In consequence, we give a complete characterization of hyperbolic 3-manifolds admitting stable maps with the stable map complexity 1 in terms of Dehn surgeries. We also discuss an estimation of the hyperbolic volume by this complexity. This is joint work with Masaharu Ishikawa (Tohoku University).