Past Junior Topology and Group Theory Seminar

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.

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.

We will look at CAT(0) spaces, their isometries and boundaries (defined through Busemann functions).