Linial Meshulam Complexes 2

Last week we defined the Linial--Meshulam model for random 2 dimensional simplicial complexes and discussed two notions of connectivity for it: Vanishing of its 1st cohomology with F2 coefficients, and vanishing of its fundamental group. This time we will focus on property (tau), namely expansion of all its finite covering spaces, and questions about the stability versus soficity of its fundamental group.

Again, all notions from algebraic topology and group theory will be explained and not assumed to be known ahead of time.