Related papers: Complete hyperbolic structures in the complement o…

We prove that if two cusped hyperbolic $3$-manifolds admit a regular isomorphism between the profinite completions of their fundamental groups, then they share the same $A$-polynomial and their strongly detected boundary slopes match up.

In this paper, we mainly study hyperbolic semigroups from which we get non-empty escaping set and Eremenko's conjecture remains valid. We prove that if each generator of bounded type transcendental semigroup S is hyperbolic, then the…

This paper investigates the strength of the trace field as a commensurability invariant of hyperbolic 3-manifolds. We construct an infinite family of two-component hyperbolic link complements which are pairwise incommensurable and have the…

In this work, we are concerned with hierarchically hyperbolic spaces and hierarchically hyperbolic groups. Our main result is a wide generalization of a combination theorem of Behrstock, Hagen, and Sisto. In particular, as a consequence, we…

Let S be a closed surface of genus at least 2. We show that a finitely generated group G which is an extension of the fundamental group H of S is word hyperbolic if and only the orbit map of the quotient group G/H on the complex of curves…

In this paper we study the structure of cohomology spaces for the Frobenius kernels of unipotent and parabolic algebraic group schemes and of their quantum analogs. Given a simple algebraic group $G$, a parabolic subgroup $P_J$, and its…

The fundamental theorem of symmetric polynomials over rings is a classical result which states that every unital commutative ring is fully elementary, i.e. we can express symmetric polynomials with elementary ones in a unique way. The…

This text brings to an end the classification of non-reduced parabolic subgroups in positive characteristic, especially two and three: they are all obtained as intersections of parabolics having maximal reduced part. We prove this result…

We give a combinatorial criterion that implies both the non-strong relative hyperbolicity and the one-endedness of a finitely generated group. We use this to show that many important classes of groups do not admit a strong relatively…

In this paper we are interested in computing representations of the fundamental group of a 3-manifold into PSL(3;C) (in particular in PSL(2;C); PSL(3;R) and PU(2; 1)). The representations are obtained by gluing decorated tetrahedra of…

In this article we characterize the complex hyperbolic groups that leave invariant a copy of the Veronese curve in $\Bbb{P}^2_{\Bbb{C}}$. As a corollary we get that every discrete compact surface group in $\PO^+(2,1)$ admits a deformation…

The study of the poset of hyperbolic structures on a group $G$ was initiated in a paper by C.Abbott, S.Balasubramanya and D.Osin. However, this poset is still very far from being understood and several questions remain unanswered. In this…

By work of Howlett and Muraleedaran--Taylor, a parabolic subgroup of a real or complex reflection group always admits a complement in its normalizer. In this note, we investigate this phenomenon for quaternionic reflection groups. Here, in…

We prove that a quasiconformal map of the 2-sphere admits a harmonic quasi-isometric extension to the 3-dimensional hyperbolic space, thus confirming the well known Schoen Conjecture in dimension 3.

We show that for given four points in the Riemann sphere and a given isotopy class of two disjoint arcs connecting these points in two pairs, there exists a unique configuration with the property that each arc is a hyperbolic geodesic…

We construct pairs of non-isometric hyperbolic 3-orbifolds with the same topological type and volume. Topologically these orbifolds are mapping tori of pseudo-Anosov maps of the surface of genus 2, with singular locus a fibred (hyperbolic)…

We consider the problem of existence of semistable systems of Hodge bundles with parabolic structure over a finite set $S \subset \mathbb P^1$ of type $(1,n)$. That is, we consider parabolic Higgs bundles $(\mathcal E, \theta)$, where…

We describe four hyperbolic knot complements in $\mathbb{S}^3$, each of which covers a prism orbifold: the quotient of $\mathbb{H}^3$ by the action of a discrete group generated by reflections in the faces of a polyhedron that has the…

We investigate positive-dimensional closed reductive subgroups of almost simple algebraic groups containing a regular unipotent element. Our main result states that such subgroups do not lie inside proper parabolic subgroups unless possibly…

We prove that there exists a holomorphic symplectic isomorphism between the rank 2 and 3 representations of the Painleve systems in the Dolbeault complex structure, and give explicit descriptions of the corresponding elliptic fibrations.…