Micael Toledo: Unstable maniplexes

Abstract: Every non-bipartite graph X admits a canonical double cover D(X) isomorphic to the direct product of X with the complete graph on two vertices. We say X is stable if all the symmetries of D(X) come from a symmetry of X, and we say it is unstable otherwise. The problem of determining whether a graph is stable or unstable is generally very difficult, and a significant amount of research has been conducted on the subject. In this talk, we consider this problem in a more geometric setting, and explore the instability of highly symmetric maps on surfaces and their generalisations to higher dimensions, which are called maniplexes.