Presented by: 
Thomas A. McCourt, University of Bristol
Tue 3 Sep, 3:00 pm - 4:00 pm
Room 442, Building 67

Let G be a triangulation of the sphere with vertex set V, such that the faces of the triangulation are properly coloured black and white. Motivated by applications in the theory of bitrades, Cavenagh and Wanless defined A_W to be the abelian group generated by the set V, with relations r+c+s = 0 for all white triangles with vertices r, c and s. The group A_B can be defined similarly, using black triangles.

In 2009 Cavenagh and Wanless conjectured that these two groups are isomorphic. In this talk we will discuss the motivation for the definitions of A_W and A_B and a proof of the conjecture. 

This is joint work with Simon Blackburn (Royal Holloway).