This blog is intended to document the progress we make in understanding the concept of a regular map. If we’re lucky, it might lead to a paper. In the short term, most of our posts will discuss results already in the literature; as time goes by, we may discuss possible avenues for new research.
The great thing about regular maps (and it’s one of the reasons why we decided to investigate them together, despite our disparate mathematical backgrounds) is that one can approach them from a number of different avenues: via (for instance) algebraic topology, combinatorial and algebraic graph theory, hyperbolic geometry, surface groups and Riemann surfaces, or geometric group theory. None of us are experts in all of these areas so we may well intersperse posts on regular maps with posts discussing useful background concepts.
Anyone should feel free to comment on what we write; we’d be very glad if regular-map-experts were to visit this blog occasionally and tell us when we’re talking nonsense. If you would like to write a post on any subject relating to regular maps, then that would be splendid. You can email us as follows:
Our usernames: n.gill; ian.short; r.brignall;
Followed by: [at] open [dot] ac [dot] uk.