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TZID:Europe/Vienna
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DTSTART:20180325T030000
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DTSTAMP:20200920T034624Z
UID:59e3891f75e72367011984@ist.ac.at
DTSTART:20180530T130000
DTEND:20180530T133000
DESCRIPTION:Speaker: Kristof Huszar\nhosted by Herbert Edelsbrunner\nAbstra
ct: On the Treewidth of Triangulated 3-Manifolds(Kristf Huszr\, Jonathan S
preer and Uli Wagner) In graph theory\, as well as in 3-mani
fold topology\, there exist several width-type parameters to describe how
"simple" or "thin" a given graph or 3-manifold is. These parameters\, such
as pathwidth or treewidth for graphs\, or the concept of thin position fo
r 3-manifolds\, play an important role when studying algorithmic problems\
; in particular\, there is a variety of problems in computational 3-manifo
ld topology - some of them known to be computationally hard in general - t
hat become solvable in polynomial time as soon as the dual graph of the in
put triangulation has bounded treewidth. In view of these algorithmic resu
lts\, it is natural to ask whether every 3-manifold admits a triangulation
of bounded treewidth. We show that this is not the case\, i.e.\, that the
re exists an infinite family of closed 3-manifolds not admitting triangula
tions of bounded pathwidth or treewidth. We derive these results from work
of Agol and of Scharlemann and Thompson\, by exhibiting explicit connecti
ons between the topology of a 3-manifold M on the one hand and width-type
parameters of the dual graphs of triangulations of M on the other hand\, a
nswering a question that had been raised repeatedly by researchers in comp
utational 3-manifold topology. In particular\, we show that if a closed\,
orientable\, irreducible\, non-Haken 3-manifold M has a triangulation of t
reewidth (resp. pathwidth) k then the Heegaard genus of M is at most 48(k+
1) (resp. 4(3k+1)).
LOCATION:Mondi Seminar Room 3\, Central Building\, IST Austria
ORGANIZER:hwagner@ist.ac.at
SUMMARY:GeomTop Seminar: short talk "\;On the Treewidth of Triangulate
d 3-Manifolds"\;
URL:https://talks-calendar.app.ist.ac.at/events/1266
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