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).