[Binghamton Geometry/Topology Seminar] Geometry/Topology 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: 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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