Maximal oriented Wicks forms

This board was created by Stacey Aston, a PhD student at Newcastle University. She is doing research in the area of geometric group theory and was trying to work through one of her supervisor’s papers on maximal oriented Wicks forms.

A Wicks form is a word on the fundamental group of a graph on a surface (and it seems that nobody has written a Wikipedia article about it yet!). For genus 1 surfaces, the maximal oriented Wicks form is abc^-1a^-1b^-1c, a word of length 6 (that can be written as a single commutator, which is a fun challenge). The maximal oriented Wicks form of a surface with 2 holes is 18 letters long, and then the word on a genus 4 surface has over 13000 letters!

[Many thanks to Christian Perfect for sending me in this photo and explanation.]