[Binghamton Geometry Topology Seminar] Geometry and Topology seminar: Matt Zaremsky

[Cary Malkiewich]

Hi everyone,

This week we are pleased to have Matt Zaremsky (SUNY Albany) speaking about
right-angled Coxeter groups, title and abstract below. As usual, the talk
will be on Thursday at 2:50pm in WH 100E.

The speaker will be delivering the talk remotely, and we'll project it in
WH 100E. In case you can't make it and would like to join remotely, you can
join at the link:

https://binghamton.zoom.us/j/94800072611

Best,
Cary

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Title: Higher virtual algebraic fibering of certain right-angled Coxeter
groups
Abstract: A group is said to “virtually algebraically fiber” if it has a
finite index subgroup admitting a map onto Z with finitely generated
kernel. Stronger than finite generation, if the kernel is even of type F_n
for some n then we say the group “virtually algebraically F_n-fibers”.
Right-angled Coxeter groups (RACGs) are a class of groups for which the
question of virtual algebraic F_n-fibering is of great interest. In joint
work with Eduard Schesler, we introduce a new probabilistic criterion for
the defining flag complex that ensures a RACG virtually algebraically
F_n-fibers. This expands on work of Jankiewicz–Norin–Wise, who developed a
way of applying Bestvina–Brady Morse theory to the Davis complex of a RACG
to deduce virtual algebraic fibering. We apply our criterion to the special
case where the defining flag complex comes from a certain family of finite
buildings, and establish virtual algebraic F_n-fibering for such RACGs. The
bulk of the work involves proving that a “random” (in some sense)
subcomplex of such a building is highly connected, which is interesting in
its own right.
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