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We show that for a fixed k, Gromov random groups with any positive density have no non-trivial degree-k representations over any field, a.a.s. This is especially interesting in light of the results of Agol, Ollivier and Wise that when the density is less than 1/6 such groups have a faithful linear representation over the rationals, a.a.s.
The minimal base size $b(G)$ for a permutation group $G$, is a widely studied topic in the permutation group theory. Z. Halasi and K. Podoski proved that $b(G)leq 2$ for coprime linear groups. Motivated by this result and the probabilistic method use
We prove a generalization of a conjecture of C. Marion on generation properties of finite groups of Lie type, by considering geometric properties of an appropriate representation variety and associated tangent spaces.
We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called weakly maximal representations. They are defined in terms of invariants in bounded cohomology and extend considerably the scope of maxim
This is an expository book on unitary representations of topological groups, and of several dual spaces, which are spaces of such representations up to some equivalence. The most important notions are defined for topological groups, but a special att
We introduce a model for random groups in varieties of $n$-periodic groups as $n$-periodic quotients of triangular random groups. We show that for an explicit $d_{mathrm{crit}}in(1/3,1/2)$, for densities $din(1/3,d_{mathrm{crit}})$ and for $n$ large