Geometry and Analysis on Groups Research Seminar

"Geometry and Analysis on Groups" Research Seminar

Time: 21.03.16, 15:00–17:00
Location: Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock
Title: Non-orderability of random triangular groups by using random 3CNF formulas
Speaker: Damian Orlef (IMPAN)
Abstract: A random group in the triangular binomial model is given by a presentation with n generators and a random set R of cyclically reduced relators of length 3, with each relator included in R independently with probability p. As n tends to infinity, the asymptotic properties of these groups vary widely with the choice of p=p(n). By Antoniuk-Luczak-Swiatkowski and Zuk, there exist threshold functions q, q' and a constant C such that a random triangular group is asymptotically almost surely (a.a.s.) free if \(q>p\) and a.a.s. infinite, hyperbolic, but not free, if \(q'>p>Cq\). We generalise the second statement by finding a constant \(c\) such that if \(q'>p>cp\), then a random triangular group is a.a.s. not left-orderable. We prove this fact by linking left-orderability of a random triangular group to the satisfiability of the random propositional formula, constructed directly from its presentation. The left-orderability of quotients will be also discussed.