Automorphism groups of Cayley maps
by
Robert Jajcay
Indiana State University
Coauthors: R.B. Richter (University of Waterloo), J. Siran (Slovak University of Technology), T.W. Tucker (Colgate University), M.E. Watkins (Syracuse University)

A Cayley map M is a 2-cell embedding of a Cayley graph C(G, X) in an orientable surface that satisfies the property that each left multiplication by an element g in G is also a map automorphism of M , i.e., G_L <= Aut(M) .

In our talk, we will describe the structure of the full automorphism group of a Cayley map M in terms of the underlying group G and a special identity-preserving permutation of G called a skew-morphism, and we will show several applications of this new way of representing the automorphism group Aut(M) to new as well as well-known problems concerning Cayley maps.

Date received: November 14, 2000