The Weigold--Goldman Conjecture for Compact Lie Groups

Let n greater than 2. Weigold conjectured that if G is a finite simple group then the product replacement graph on n-generating tuples is connected (which also implies that it is an expander for n greater than 3). This conjecture is still (wide) open. I will discuss analog problems when G is a compact Lie group. More precisely, I will present the little that I know and speculate about stronger conjectures that I cannot prove.