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CATEGORIES:Geometry and Mathematical Physics seminar
SUMMARY:Algebraic and combinatorial decompositions of Fuch
sian groups - Daniel Labardini Fragoso\, Universid
ad Nacional Autónoma de México
DTSTART:20200124T150000Z
DTEND:20200124T160000Z
UID:TALK4106AT
URL:/talk/index/4106
DESCRIPTION:The discrete subgroups of PSL_2(*R*) are often cal
led 'Fuchsian groups'. For\nFuchsian groups \\Gamm
a whose action on the hyperbolic plane H is free\,
the\norbit space H/\\Gamma has a canonical struct
ure of Riemann surface with a\nhyperbolic metric\,
whereas if the action of \\Gamma is not free\, th
en\nH/\\Gamma has a structure of 'orbifold'. In th
e former case\, there is a\ndirect and very clear
relation between \\Gamma and the fundamental group
\n\\pi_1(H/\\Gamma\,x): a theorem of the theory of
covering spaces states that\nthey are isomorphic.
When the action of \\Gamma is not free\, the rela
tion\nbetween \\Gamma and \\pi_1(H/\\Gamma\,x) is
subtler. A 1968 theorem of\nArmstrong states that
there is a short exact sequence\n1->E->\\Gamma->\\
pi_1(H/\\Gamma\,x)->1\, where E is the subgroup of
\\Gamma\ngenerated by the elliptic elements. For
\\Gamma finitely generated\,\nnon-elementary and w
ith at least one parabolic element\, I will presen
t\nfull algebraic and combinatorial decompositions
of \\Gamma in terms of\n\\pi_1(H/\\Gamma\,x) and
a specific finitely generated subgroup of E\, thus
\nimproving Armstrong's theorem.\n\nThis talk is b
ased on an ongoing joint project with Sibylle Schr
oll and\nYadira Valdivieso-Díaz that aims at descr
ibing the bounded derived\ncategories of skew-gent
le algebras in terms of curves on surfaces with\no
rbifold points of order 2.
LOCATION:Lecture Theatre B\, Watson Building
CONTACT:Timothy Magee
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