Geometry Seminar
Fall 2021
Thursdays 3:00-4:00pm, in
Ryerson classrooms and sometimes on Zoom
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- Thursday December 2 at 3:00PM-4:00PM in Zoom (see email for link)
- Yael Algom-Kfir, Haifa University
- Nielsen realization for big Out(Fn)
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Abstract: (Joint with M. Bestvina.) We propose to
study the group PMaps(X) of proper homotopy
equivalences of X a locally finite (infinite)
graph. We prove that this is a Polish group, in fact
isomorphic to the irrationals. We then prove the Nielsen
realization theorem in this context, i.e. if H is
a compact subgroup then there is a locally finite graph
Y proper homotopy equivalent to X, so
that under the isomorphism PMaps(X) â‰
PMaps(Y) the group H maps to a group
represented by automorphisms of the graph Y.
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- Thursday November 18 at 3:00PM-4:00PM in Ryerson 177
- Justin Lanier, University of Chicago
- Big surfaces and Nielsen realization
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Abstract: This is a talk to give some background and
context for Yael Algom-Kfir’s upcoming talk. We will
discuss the classification of 2-manifolds, which includes
surfaces whose fundamental groups are not finitely
generated. We will also discuss topologies on the mapping
class groups of these surfaces. Finally we’ll discuss the
Nielsen realization theorem for finite subgroups of these
mapping class groups by Afton–Calegari–Chen–Lyman, as
well as Nielsen realization (by graph isomorphisms) for
finite subgroups of Out(Fn).
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- Thursday November 11 at 3:00PM-4:00PM in Ryerson 176
- Michael Klug, University of Chicago
- How not to study low-dimensional topology?
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Abstract: Stallings gave a group-theoretic approach
to the 3-dimensional Poincaré conjecture that was later
turned into a group-theoretic statement equivalent to the
Poincaré conjecture by Jaco and Hempel and then proven by
Perelman. Together with Blackwell, Kirby, Longo, and Ruppik,
we have extended Stallings's approach to give
group-theoretically defined sets that are in bijection with
(i) closed 3-manfiolds, (ii) closed 3-manifolds with a link,
(iii) closed 4-manifolds, and (iv) closed 4-manifolds with a
link (of surfaces). I will explain these sets and these
bijections (which use Heegaard/bridge splittings in the
3-dimensional setting and trisections/surface bridge
splittings in the 4-dimensional setting).
Due to the high number of requests, we are no longer accepting speakers via self-invitations.
For questions, contact