[Binghamton Geometry/Topology Seminar] Topology/Geometry Seminar this Thursday

[Tam Nguyen Phan]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

   Date: Thursday, October 29th, 2015

   Time:  2.50 pm

   Place: Whitney Hall, Room 100E,  followed by coffee/tea in the
      Hilton Reading Room. Note the new location of the math department (
http:// <http://www2.math.binghamton.edu/p/directions>www2.
<http://www2.math.binghamton.edu/p/directions>math.binghamton.edu
<http://www2.math.binghamton.edu/p/directions>/p/directions
<http://www2.math.binghamton.edu/p/directions>).

   Speaker:  *Anisah Nu'Man*  (Trinity College)

   Title:  *Intrinsic tame filling functions*

    Abstract: (pdf also attached)

Let $G$ be a group with a finite presentation $P = \langle A|R \rangle$
such that $A$ is inverse-closed. Let $f \colon  \mathbb{N}[\frac{1}{4}]
\rightarrow \mathbb{N}[\frac{1}{4}]$ be a nondecreasing function. Loosely,
$f$ is an intrinsic tame filling function for $(\mathcal{G},\mathcal{P})$
if for every word $w$ over $A^∗$ that represents the identity element in
$G$, there exists a van Kampen diagram $\triangle$ for $w$ over $P$ and a
continuous choice of paths from the basepoint ∗ of $\triangle$ to the
boundary of $\triangle$ such that the paths are steadily moving outward as
measured by $f$. The isodiametric function (or intrinsic diameter function)
introduced by Gersten and the extrinsic diameter function introduced by
Bridson and Riley are useful invariants capturing the topology of the
Cayley complex. Tame filling functions are a refinement of the diameter
functions introduced by Brittenham and Hermiller and are used to gain
insight on how wildly maximum distances can occur in van Kampen diagrams.
Brittenham and Hermiller showed that tame filling functions are a
quasi-isometry invariant and that if $f$ is an intrinsic (respectively
extrinsic) tame filling function for $(\mathcal{G},\mathcal{P})$, then
$(\mathcal{G},\mathcal{P})$ has an intrinsic (respectively extrinsic)
diameter function equivalent to the function $n \rightarrow [f(n)]$. In
contrast to diameter functions, it is unknown if every pair
$(\mathcal{G},\mathcal{P})$ has a finite-valued tame filling function. In
this talk I will discuss intrinsic tame filling functions for graph
products (a generalization of direct and free products) and certain free
products with amalgamation.

NOTE:  The seminar has a webpage where the semester's program is listed:

http://www2.math.binghamton.edu/p/seminars/topsem
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