The N+2nd Southern California Topology Conference

Saturday April 30th, 2005


At Caltech, in Room 151 of the Sloan Building. Here's a map.


in the faculty parking lot across California from Sloan, bordering the excavation. (Note there is also parking at the back of the lot, behind the tennis courts). Street parking is also available on California, and on Wilson.


If you need a hotel, the Saga is a good yet inexpensive choice.

Getting to Pasadena by air:

Even if you don't live in Southern California, you're still welcome to come. The most convenient airport to Pasadena is Burbank, but it's certainly not worth changing planes to get there over the canonical LAX. For those you Northern California folks, Southwest has frequent service from Oakland, San Jose, and Sacramento to Burbank. Ontario and Long Beach airports are also reasonable choices, but ground transit from them to Pasadena is more expensive. For all airports, you can use SuperShuttle to get to Pasadena (about $20 one-way for Burbank, $30 for LAX and $50 + for the other two).

Coffee and bagels available outside 151 Sloan, 10-10:30 am

Schedule of talks:

Speaker Time Title
Hossein Namazi, Yale 10:30-11:30 am Heegaard Splittings and Hyperbolic Geometry
Mladen Bestvina, Utah 1:30-2:30 pm The Torelli subgroup of Out(Fn)
Pete Storm, Stanford 2:45-3:45 pm Lower volume bounds for hyperbolic 3-manifolds with boundary
Hyam Rubinstein, Melbourne 4-5 pm Separating incompressible surfaces are abundant in 3-manifolds.

Abstracts of talks:

Hossein Namazi: Heegaard Splittings and Hyperbolic Geometry

It is well known that every compact orientable 3-manifold admits a Heegaard splitting, but using the "combinatorics" of these splittings to describe the topology of the manifold has proved elusive. Hempel introduced a "handlebody distance" for Heegaard splittings and conjectured that when this distance is sufficiently large the manifold should be hyperbolic. Examples of 3-manifolds with large handlebody distance were constructed by Kobayashi and Luo. Using hyperbolic geometry, we prove that these and in fact a bigger class of 3-manifolds which satisfy a more general combinatorial property are "almost hyperbolic", i.e. they admit Riemannian metrics with sectional curvature close to -1. We will also mention some topological corollaries of this construction which were subject of a joint work with Juan Souto.

Mladen Bestvina: The Torelli subgroup of Out(Fn)

The group in the title is the kernel of the natural map Out(Fn)-> GL(n, Z). As for the classical mapping class group counterparts (except for the work of Mess in low genus), the basic features such as the dimension and finiteness properties are unknown. I will describe an approach to an understanding to these groups that leads to a complete success when n=3 and to at least a partial success when n=4. This work is joint with Kai-Uwe Bux and Dan Margalit, and is still in progress.

Pete Storm: Lower volume bounds for hyperbolic 3-manifolds with boundary

Nontrivial lower volume bounds can sometimes be obtained in terms of the decomposition of a hyperbolic 3-manifold with boundary into its geometric pieces. The main technique is the barycenter method, which is used like a replacement for harmonic maps. Perelman's work also raises the possibility of obtaining new volume information about closed Haken hyperbolic 3-manifolds via their infinite covers.

Hyam Rubinstein: Separating incompressible surfaces are abundant in 3-manifolds.

This is joint work with Kazuhiro Ichihara and Makoto Ozawa. We give a construction showing that "most" closed orientable irreducible or compact orientable irreducible 3-manifolds with incompressible tori boundary have embedded closed separating non peripheral incompressible surfaces. The key idea is to first attached all the separating handles for a minimal genus Heegaard splitting. The resulting 3-manifold is shown to always have many non peripheral separating incompressible surfaces. These survive most ways of attaching the non separating handles. Moreover, the method gives an interesting test (but not an algorithm) to find such surfaces. For 3-manifolds of Heegaard genus 2, we discuss in detail how separating incompressible surfaces arise in most cases.

Recreational activities:

Lunch at one of the fine restaurants on Lake Street. Francis Bonahon will be hosting the aftermath party at his home at 1400 S. Third Avenue in neighboring Arcadia. Here's a map of how to get there from Caltech.


Nathan Dunfield.