María del Río Francos: Symmetry type graphs of maps and maniplexes

Povzetek. Topologically, a map can be defined as the cellular embedding of a connected graph on a closed surface. A maniplex M of rank n-1 is the combinatorial generalization of a map, whose structure is completely determined by an edge-colored n-valent graph G(M) with chromatic index n, often called the flag graph. In particular, non-degenerated maps correspond to maniplexes of rank 2.

In this talk we will describe and give some properties of the symmetry type graph of a maniplex M. This latter corresponds to the quotient graph of the flag graph G(M) under the action of the automorphism group of M.