Geometric group theory seminar - 2017/18
The seminar meets each Wednesday at 3 PM in BURN 920
McGill GGT research group
September 6, 2017: Stéphane Lamy (Université Paul Sabatier), Signature morphisms on the Cremona group.
The Cremona group is the group of birational symmetries of the
plane. This is a rather huge group, which is neither finitely generated
nor finite dimensional.
The abelianization of the Cremona group was recently studied: over the
base field C, the abelianization is trivial, but over R, the
abelianization is an uncountable direct sum
of Z/2. I will discuss similar results over more general fields, such as
number fields or finite fields. The key is to use a natural action on a
square complex, to exhibit various trees as quotients or subcomplexes,
and then to apply Bass-Serre theory (joint work with Susanna Zimmermann).
September 27, 2017: Sang-hyun Kim (Seoul National University), Free products in Diff(S1).
We prove that if G is a finitely generated non-virtually-abelian group,
then (G x Z) * Z does not embed into Diff^2(S^1). In particular, the class
of subgroups of Diff^r(S^1) is not closed under taking free products for
each r >= 2. We complete the classification of RAAGs embeddable in
Diff^r(S^1) for each r, answering a question in a paper of M. Kapovich.
(Joint work with Thomas Koberda)
Seminar schedule archive