Infinitely many quasi-arithmetic maximal reflection groups

2021/09/07 by Dotti, Edoardo, Kolpakov, Alexander
#11R06 #20H10 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2109.03316

Abstract

In contrast to the fact that there are only finitely many maximal arithmetic reflection groups acting on the hyperbolic space ℍⁿ, n≥ 2, we show that: (a) one can produce infinitely many maximal quasi-arithmetic reflection groups acting on ℍ²; (b) they admit infinitely many different fields of definition; (c) the degrees of their fields of definition are unbounded. However, for n≥ 14 an approach initially developed by Vinberg shows that there are still finitely many fields of definitions in the quasi-arithmetic case.

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