7 problems

A hyperbolic manifold is arithmetic when its fundamental group is an arithmetic lattice. A subgroup is geometrically finite if its convex core has finite volume, and a lattice is G…

Let $F_2=\langle x,y\rangle$ be the free group of rank two, and let $u(x,y),v(x,y)$ be normal generators of $F_2$. For a finite factor group $G$ of $F_2$, write $\bar x,\bar y$ and…

Let $G$ be a torsion-free nilpotent group, and let $\delta$ be the constant in the previously established upper bound for the residual finiteness growth $\operatorname{RF}_G$. Exac…

A quandle is an algebraic structure with its standard quandle operation, and a quandle is residually finite if distinct elements can be separated by homomorphisms to finite quandle…

A Gromov hyperbolic group is a group satisfying the usual metric hyperbolicity condition; a group is residually finite if its nontrivial elements survive in finite quotients, and i…

Let $M^n$ be a closed aspherical $n$-manifold with residually finite fundamental group. Let $\Gamma_k\vartriangleleft\pi_1(M^n)$ be any normal chain with $\bigcap_k\Gamma_k=1$. Lüc…

Involutory quandles are finitely residual. If $IQ(D)$ is non-trivial, then there is a finite non-trivial involutory quandle $Q$ and a surjective homomorphism