arXiv research

We give a quantification of residual finiteness for the fundamental groups of hyperbolic manifolds that admit a totally geodesic immersion to a compact, right-angled Coxeter orbifold of dimension 3 or 4. Specifically, we give explicit upper bounds on residual finiteness that are linear in terms of geodesic length. We t…

Study gives bounds on subgroup indices and geodesic residual finiteness for hyperbolic 3-manifolds.

The study proves residual finiteness for certain lattice extensions and negatively curved projective varieties.

We quantify Peter Scott's Theorem that surface groups are locally extended residually finite (LERF) in terms of geometric data. In the process, we will quantify another result by Scott that any closed geodesic in a surface lifts to an embedded loop in a finite cover.

Abstract commensurators linked to topological models of solenoids.

Study geodesic flows on hyperbolic manifolds without conjugate points, proving unique measure of maximal entropy.

Link quandles are shown to be residually finite.

Free and knot quandles are residually finite.

Abstract: Non-residually finite hyperbolic groups imply non-residually finite rigid hyperbolic groups.

The study examines free products of hyperbolic manifold groups and their model geometries.

Motivated by the results of Scott and Patel about "untangling" closed geodesics in finite covers of hyperbolic surfaces, we introduce and study primitivity, simplicity and non-filling index functions for finitely generated free groups. We obtain lower bounds for these functions and relate these free group results back …

In every conformal class of Finsler (or Riemannian) metrics on a closed manifold there exists a residual subset of Finsler metrics, such that, with respect to the residual Finsler metrics, in any non-trivial homotopy class of free loops there is precisely one shortest geodesic loop.

Study on endomorphism and automorphism groups of specific quandles.

For n>3 we study spaces obtained from finite volume complete real hyperbolic n-manifolds by removing a compact totally geodesic submanifold of codimension two. We prove that their fundamental groups are relative hyperbolic, co-Hopf, biautomatic, residually hyperbolic, not Kähler, not isomorphic to lattices in virtually…

We show that Out(G) is residually finite if G is a one-ended group that is hyperbolic relative to virtually polycyclic subgroups. More generally, if G is one-ended and hyperbolic relative to proper residually finite subgroups, the group of outer automorphisms preserving the peripheral structure is residually finite. We…

Proves Singer conjecture for graph manifolds with residually finite groups.

Given a prime $p$, a group is called residually $p$ if the intersection of its $p$-power index normal subgroups is trivial. A group is called virtually residually $p$ if it has a finite index subgroup which is residually $p$. It is well-known that finitely generated linear groups over fields of characteristic zero are …

Many 2D Artin groups are residually finite.

The study examines discrete subgroups of Lie groups and their residual finiteness.

Study of uncountable family of finitely generated groups.

Proves Singer conjecture for specific geometric varieties.

ResNets learn the geodesic curve in Wasserstein space.

The paper proves residual finiteness of certain lattices and constructs surfaces with specific fundamental groups.

We study spaces obtained from a complete finite volume complex hyperbolic n-manifold M by removing a compact totally geodesic complex (n-1)-submanifold. The main result is that the fundamental group of M-S is relatively hyperbolic, relative to fundamental groups of the ends of M-S, and M-S admits a complete finite volu…

We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable relatively hyperbolic group is residually finite. As a direct consequence, we obtain that the outer automorphism group of a limit group is residually finite.

The fundamental n-quandles of links are residually finite for n ≥ 2.

We show that there is no algorithm deciding whether the maximal residually free quotient of a given finitely presented group is finitely presentable or not. Given a finitely generated subgroup G of a finite product of limit groups, we discuss the possibility of finding an explicit set of defining equations (i.e. of exp…

Artin groups have finite stature based on vertex groups.

Let $G$ be a virtually special group. Then the residual finiteness growth of $G$ is at most linear. This result cannot be found by embedding $G$ into a special linear group. Indeed, the special linear group $\text{SL}_k(\mathbb{Z})$, for $k > 2$, has residual finiteness growth $n^{k-1}$.

Every non-trivial knot group is fully residually perfect.

Proves congruence subgroup property for mapping class groups of hyperbolic surfaces.

The study examines Hopfian properties of conjugation quandles and their underlying groups.

Study compact Willmore surfaces without complex structure convergence, computing energy loss and geodesic lengths.

Residually finite groups found in manifold automorphisms.

New proof shows RFRS groups virtually fibred if their $L^2$-Betti number vanishes.

We prove that if every hyperbolic group is residually finite, then every quasi-convex subgroup of every hyperbolic group is separable. The main tool is relatively hyperbolic Dehn filling.

Study geodesics on flat tori, focusing on convex bodies.

Groups with similar pro-$p$ completions have two-generated subgroups that are free.

We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable hyperbolic group is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated Fuchsian group and of every free-by-finite group is resudually finite. We…

Non-isomorphic groups with similar profinite completions found.

New examples of hyperbolic 3-manifolds with unique profinite structure.

Triangle groups uniquely identified by their finite quotients.

Proves 3D Poincaré duality groups without property (T)

Constructs minimal laminations with controlled leaf topologies.

New groups with special properties found.

Two groups with same profinite completion have different co-Hopfian properties.

A new method, Residual-Permuted Sums, improves confidence region construction for linear regression models.

Study on profinite rigidity of direct products of free and surface groups.