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CATEGORIES:Geometric Group Theory (GGT) Seminar
SUMMARY:Counting incompressible surfaces in 3-manifolds -
Nathan Dunfield (University of Illinois)
DTSTART;TZID=Europe/London:20200214T134500
DTEND;TZID=Europe/London:20200214T144500
UID:TALK134986AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/134986
DESCRIPTION:Counting embedded curves on a hyperbolic surface a
s a function of their length has been much studied
by Mirzakhani and others. I will discuss analogou
s questions about counting incompressible surfaces
in a hyperbolic 3-manifold\, with the key differe
nce that now the surfaces themselves have intrinsi
c topology. As there are only finitely many incomp
ressible surfaces of bounded Euler characteristic
up to isotopy in a hyperbolic 3-manifold\, it make
s sense to ask how the number of isotopy classes g
rows as a function of the Euler characteristic. Us
ing Hakenâ€™s normal surface theory and facts about
branched surfaces\, we can characterize not just t
he rate of growth but show it is (essentially) a q
uasi-polynomial. Moreover\, our method allows for
explicit computations in reasonably complicated ex
amples. This is joint work with Stavros Garoufalid
is and Hyam Rubinstein.
LOCATION:CMS\, MR13
CONTACT:
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