## The Redbud Topology Conference- October 26, 2013, Oklahoma State University

This conference was a local conference bringing together mathematicians from schools in the Redbud region", especially University of Oklahoma, Oklahoma State University, and University of Arkansas.

## Speakers:

Max Forester (OU)
Yoe Herrera (OU)
Yo'av Rieck (UArk)
Trent Schirmer (OSU)

## Abstracts:

Max Forester - A gap theorem for stable commutator length

I will discuss some recent results on stable commutator length in Baumslag-Solitar groups. I will show how to construct efficient quasimorphisms for groups acting on trees, and will give some further arguments that are specific to the Bass-Serre trees of Baumslag-Solitar groups.
This is joint work with Matt Clay and Joel Louwsma.

Yoe Herrera - Intersection numbers in a hyperbolic surface

Abstract: For a compact surface $S$ with constant negative curvature $-\kappa$ (for some $\kappa>0$) and genus $\mathfrak g\geq2$, we show that the tails of the distribution of $i(\alpha,\beta)/l(\alpha)l(\beta)$ (where $i(\alpha,\beta)$ is the intersection number of the closed geodesics $\alpha$ and $\beta$ and $l(\cdot)$ denotes the geometric length) are estimated by a decreasing exponential function. As a consequence, we find the asymptotic normalized average of the intersection numbers of pairs of closed geodesics on $S$. In addition, we prove that the size of the sets of geodesics whose $T$-self-intersection number is not close to $\kappa T^2/(2\pi^2(\mathfrak g-1))$ is also estimated by a decreasing exponential function. And, as a corollary of the latter, we obtain a result of Lalley which states that most of the closed geodesics $\gamma$ on $S$ with $l(\gamma)\leq T$ have roughly $\kappa l(\gamma)^2/(2\pi^2(\mathfrak g-1))$ self-intersections, when $T$ is large.

Yo'av Rieck - The link volume of hyperbolic 3-manifolds and cosmetic surgery on links

Abstract: The link volume is an invariant of closed orientable 3-manifolds that measures how efficiently a manifold can be shown as a (branched) cover of S^3. We will first define the link volume and explain its basic properties, and then explain its relationship to the link volume. To that end we will need to develop tool to study cosmetic surgery on links with arbitrarily many components.
This is joint work with Yasushi Yamashita from Nara Women's University.

Trent Schirmer - A lower bound on tunnel number subadditivity

Abstract: The tunnel number of a knot $K\subset S^3$ can be defined by the equation $t(K)+1=g(S^3\setminus \eta(K))$, where $g(\cdot)$ denotes the Heegaard genus. We prove that $t(K_1\# K_2)\geq \max\{t(K_1),t(K_2)\}$ for any pair of knots in $S^3.$ This bound is best possible.

This archive was restored in 2018 from data in our 2014 Redbud proposal and the email archives of the speakers. We thank the conference speakers their assistance. Furthermore, please email Neil Hoffman if there are inaccuracies in data such as a missing speaker.