FS≠RB

Great news this month! Yuxu Chen, Hui Kou and Zhenchao Lyu, from the University of Sichuan in Chengdu, have finally cracked the problem whether FS-domains and RB-domains are the same notion, and they are not. This problem had been open since the invention of FS-domains by Achim Jung in 1990. Every RB-domain is an FS-domain, and the issue was the reverse inclusion. Jimmie Lawson had suggested that the FS-domain Disc of discs in the plane might be a counterexample. And this is exactly what Chen, Kou and Lyu show: Disc is not an RB-domain. The proof is very inventive, and goes through the study of the matrix cone of the Lorentz cone in 2+1 dimensions, which are constructions that should be more familiar to people working in special relativity. Read the full post.