Oliver Club

Erica FlapanPomona College
Topological symmetry groups

Thursday, May 4, 2017 - 4:00pm
Malott 532

Chemists have defined the point group of a molecule as the group of rigid
symmetries of its molecular graph in $ {\mathbb R}^3 $. While this group is useful for
analyzing the symmetries of rigid molecules, it does not include all of the
symmetries of molecules which are flexible or can rotate around one or more
bonds. To study the symmetries of such molecules, we define the topological
symmetry group of a graph embedded in $ {\mathbb R}^3 $ to be the subgroup of the auto-
morphism group of the abstract graph that is induced by homeomorphisms
of $ {\mathbb R}^3 $. This group gives us a way to understand not only the symmetries
of non-rigid molecular graphs, but the symmetries of any graph embedded
in $ {\mathbb R}^3 $. The study of such symmetries is a natural extension of the study of
symmetries of knots. In this talk we will present a survey of results about
the topological symmetry group and how it can play a role in analyzing the
symmetries of non-rigid molecules.

Refreshments will be served at 3:30 PM.