Forthcoming events in this series
The Asymptotic Cone of a Symmetric Space is a Euclidean Building
Abstract
I will introduce Symmetric spaces via a result of Kleiner & Leeb, comparing the axioms in their definition of a Euclidean building with properties of symmetric spaces of noncompact type.
Delzant and Potyagailo's hierarchical accessibility
Abstract
Take a group G and split it as the fundamental group of a graph of groups, then take the vertex groups and split them as fundamental groups of graphs of groups etc. If at some point you end up with a collection of unsplittable groups, then you have a hierarchy. Haken showed that for any 3-manifold M with an incompressible surface S, one can cut M along S and and then find other incompressible surfaces in M\S and cut again, and repeating this process one eventually obtains a collection of balls. Analogously, Delzant and Potyagailo showed that for any finitely presented group without 2-torsion and a certain sensible class E of subgroups of G, G admits a hierarchy where the edge groups of the splittings lie in E. I really like their proof and I will present it.
16:00
The Alexander Polynomial
Abstract
The Alexander polynomial of a link was the first link polynomial. We give some ways of defining this much-studied invariant, and derive some of its properties.
16:00
Outer Space
Abstract
We introduce Outer space, a contractible finite dimensional topological space on which the outer automorphism group of a free group acts 'nicely.' We will explain what 'nicely' is, and provide motivation with comparisons to symmetric spaces, analogous spaces associated to linear groups.
16:00
Unknotting operations on knots and the mapping class group
16:00
CAT(0) spaces and their boundaries
Abstract
We will look at CAT(0) spaces, their isometries and boundaries (defined through Busemann functions).