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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:H_{4g-6}(M_g) - Soren Galatius (University of Cope
nhagen)
DTSTART;TZID=Europe/London:20181203T100000
DTEND;TZID=Europe/London:20181203T110000
UID:TALK115240AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/115240
DESCRIPTION:The set of isomorphism classes of genus g Riemann
surfaces carries a natural topology in which it ma
y be locally parametrized by 3g-3 complex paramete
rs. The resulting space is denoted M_g\, the modu
li space of Riemann surfaces\, and is more precise
ly a complex orbifold of that dimension. The stud
y of this space has a very long history involving
many areas of mathematics\, including algebraic ge
ometry\, group theory\, and stable homotopy theory
. The space M_g is not compact\, essentially beca
use a family of Riemann surface may degenerate int
o a non-smooth object\, and may be compactified in
several interesting ways. I will discuss a compa
ctification due to Harvey\, which looks like a com
pact real (6g-6)-dimensional manifold with corners
\, except for orbifold singularities. The combina
torics of the corner strata in this compactificati
on may be encoded using graphs. Using this compac
tification\, I will explain how to define a chain
map from Kontsevich'\;s graph complex to a chai
n complex calculating the rational homology of M_g
. The construction is particularly interesting in
degree 4g-6\, where our methods give rise to many
non-zero classes in H_{4g-6}(M_g)\, contradicting
some predictions. This is joint work with Chan a
nd Payne (arXiv:1805.10186).
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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