# Columbia Geometric Topology Seminar

## Fall 2016

The GT seminar meets on Fridays in Math 520, at 2 PM.
Organizer: Walter Neumann.
Other area seminars. Our e-mail list. Archive of previous semesters

Date Speaker Title
Friday Sept 9 Organizational meeting 2pm Room 520
September 16 Hung C Tran (UGA) Geometric embedding properties of Bestvina-Brady subgroups
September 22 THURSDAY 2:40pm! BoGwang Jeon The Unlikely Intersection Theory and the Cosmetic Surgery Conjecture
September 30  No GT seminar
October 7 Henry Segerman, Oklahoma State Connectivity of triangulations without degree one edges under 2-3 and 3-2 moves
October 14 Mehdi Yazdi (Princeton) On Thurston's Euler class one conjecture
October 21 David Hume, MSRI and Oxford TBA
November 4  No GT seminar
November 11 Tim Susse, U Nebraska TBA
November 18 Daniel Groves, UIC TBA
November 25 No Seminar Happy Thanksgiving
December 2 David Futer, Temple U TBA
December 9 Hongbin Sun, UCB TBA
Spring Semester Ahn Tran, UT Dallas

## Abstracts

Hung C Tran, UGA
September 16
Title: Geometric embedding properties of Bestvina-Brady subgroups
We compute the subgroup distortion of Bestvina-Brady subgroups. We use the result of this computation to show that for each integer $n\geq 3$, there is a free subgroup of rank $n$ of some right-angled Artin group whose inclusion is not a quasi-isometric embedding. This corollary answers the question of Carr about the minimum rank $n$ such that some right-angled Artin group has a free subgroup of rank $n$ whose inclusion is not a quasi-isometric embedding. It is also well-known that a right-angled Artin group $A_\Gamma$ is the fundamental group of a graph manifold whenever the defining graph $\Gamma$ is a tree. We show that the Bestvina-Brady subgroup $H_\Gamma$ in this case is a horizontal surface subgroup.

BoGwang Jeon, Columbia
THURSDAY September 22, 2:40pm
Title: The Unlikely Intersection Theory and the Cosmetic Surgery Conjecture
The main result of this talk is the following theorem: Let M be a 1-cusped hyperbolic 3-manifold whose cusp shape is not quadratic, and M(p/q) be its p/q-Dehn filled manifold. If p/q is not equal to p'/q' for sufficiently large |p|+|q| and |p'|+|q'|, there is no orientation preserving isometry between M(p/q) and M(p'/q'). This resolves the conjecture of C. Gordon, which is so called the Cosmetic Surgery Conjecture, for hyperbolic 3-manifolds belonging to the aforementioned class except for possibly finitely many exceptions for each manifold. We also consider its generalization to more cusped manifolds. The key ingredient of the proof is the unlikely intersection theory developed by E. Bombieri, D. Masser, and U. Zannier.

Henry Segerman, Oklahoma State U
October 7
Title: Connectivity of triangulations without degree one edges under 2-3 and 3-2 moves.
Matveev and Piergallini independently showed that, with a small number of known exceptions, any triangulation of a three-manifold can be transformed into any other triangulation of the same three-manifold with the same number of vertices, via a sequence of 2-3 and 3-2 moves. We can interpret this as showing that the "2-3 Pachner graph" of such triangulations is connected. This is useful for defining invariants of a three-manifold based on the triangulation. However, there are "would-be" invariants that can only be defined on triangulations with certain properties, for example 1-efficiency or having only essential edges. Unfortunately, there are no similar connectivity results for the subgraphs of the Pachner graph with such properties. In this talk, I will describe a new connectivity result for a weaker property than either 1-efficiency or essential edges: that of a triangulation having no degree one edges.

Mehdi Yazdi, Princeton
October 14
Title: On Thurston's Euler class one conjecture
In 1976, Thurston proved that taut foliations on closed hyperbolic 3–manifolds have Euler class of norm at most one, and conjectured that, conversely, any Euler class with norm equal to one is Euler class of a taut foliation. I construct counterexamples to this conjecture and suggest an alternative conjecture.

David Hume, MSRI and Oxford
October 21
Title: To be announced
Abstract

November 11
Title: To be announced
Abstract

Daniel Groves, University of Illinois at Chicago
November 18
Title: To be announced
Abstract

David Futer, Temple University
December 2
Title: To be announced
Abstract

Hongbin Sun, UCB
December 9
Title: To be announced
Abstract

Ahn Tran, UT Dallas
Spring Semester
Title:
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# Other relevant information.

## Previous semesters:

Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, 2010/11, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006.