arXiv research

The paper explores domains in flag manifolds with specific geometric properties.

Let G be a one-ended group acting discretely and co-compactly on a CAT(0) space X. We show that the boundary of X has no cut points and that one can detect splittings of $G$ over two-ended groups and recover its JSJ decomposition from the boundary. We show that any discrete action of a group G on a CAT(0) space X satis…

The paper proves a flat torus theorem for certain groups acting on convex domains.

The paper defines conditions for groups acting on convex domains to be relatively hyperbolic.

An open convex set in real projective space is called divisible if there exists a discrete group of projective automorphisms which acts co-compactly. There are many examples of such sets and a theorem of Benoist implies that many of these examples are strictly convex, have $C^1$ boundary, and have word hyperbolic divid…

The paper characterizes groups acting on real projective spaces.

We study a class of localized indices for the Dirac type operators on a complete Riemannian orbifold, where a discrete group acts properly, co-compactly and isometrically. These localized indices, generalizing the $L^2$-index of Atiyah, are obtained by taking certain traces of the higher index for the Dirac type operat…

3-manifold groups can only have convex co-compact representations if they are geometric or hyperbolic.

Solves classification of compact Clifford-Klein forms for specific Lie groups.

Groups with certain properties act on metric spaces with asymptotic property C.

Groups on CAT(0) cube complexes grow exponentially uniformly.

New group acts on complex but not in lower dimensions.

The study finds conditions for groups acting on CAT(0) cube complexes to have infinite girth.

Groups act on cube complexes with varying dimensions.

Study groups acting on trees with specific local actions, proving cohomology vanishing or infinite.

Study shows critical exponents for tree-acting groups.

Classifies Lie groups acting on compact Lorentz manifolds.

Groups can embed uniformly but not act properly on contractible manifolds.

Minimal surfaces with symmetries exist under certain group actions.

Hyperbolic groups act on spheres, and nearby actions are semi-conjugate.

R. S. Kulkarni showed that a finite group acting pseudofreely, but not freely, preserving orientation, on an even-dimensional sphere (or suitable sphere-like space) is either a periodic group acting semifreely with two fixed points, a dihedral group acting with three singular orbits, or one of the polyhedral groups, oc…

A special group of transformations of the real line cannot act effectively on it.

The purpose of this paper is to survey the structure of closed and transitive transformation groups acting on a closed surface. In particular, we prove a number of relations between groups acting on the sphere that contain the rotation group, together with a diagram of how these groups are connected. In addition, we de…

In the present paper we show spectral properties of a littleknown natural Riemannian second-order differential operator acting on differential forms.

Parabolic automorphisms on hyperkahler manifolds act ergodically on fibers.

Survey on groups acting on non-positive curvature spaces.

Artin-Tits groups act loxodromically on a delta-hyperbolic complex, with most elements doing so.

Proves Grothendieck-Teichmüller group acts on specific mapping class groups.

In the present paper we show properties of a little-known Laplacian operator acting on symmetric tensors. This operator is an analogue of the well known Hodge-de Rham Laplacian which acts on exterior differential forms. Moreover, this operator admits the Weitzenböck decomposition and we study it using the analytical me…

Groups acting on product trees are boundary rigid.

The main theorem is that if K is a finite CW complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X x S^n for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial t…

The Mazur pattern acts by the identity up to topological concordance.

Modeling long-range context for multi-function utterances in dialogues.

The only finite nonabelian simple group acting on a homology 3-sphere - necessarily non-freely - is the dodecahedral group $\Bbb A_5 \cong {\rm PSL}(2,5)$ (in analogy, the only finite perfect group acting freely on a homology 3-sphere is the binary dodecahedral group $\Bbb A_5^* \cong {\rm SL}(2,5)$). In the present pa…

We prove an acylindrical accessibility theorem for finitely generated groups acting on $\mathbf R$-trees. Namely, we show that if $G$ is a freely indecomposable non-cyclic $k$-generated group acting minimally and $M$-acylindrically on an $\mathbf R$-tree $X$ then for any $ε>0$ there is a finite subtree $Y_ε\subseteq X$…

New groups defined that act on trees without repeating.

The study establishes conditions for groups acting on polygonal complexes to contain virtually free subgroups.

The paper examines rigidity in geometric actions of Coxeter groups on Croke-Kleiner spaces.

Whenever the mapping class group of a closed orientable surface of genus g acts by semisimple isometries on a complete CAT(0) space of dimension less than g it fixes a point.

The famous Banach-Tarski paradox claims that the three dimensional rotation group acts on the two dimensional sphere paradoxically. In this paper, we generalize their result to show that the classical group acts on the flag manifold paradoxically.

A manifold M is locally conformally Kahler (LCK) if it admits a Kahler covering with monodromy acting by holomorphic homotheties. For a compact connected group G acting on an LCK manifold by holomorphic automorphisms, an averaging procedure gives a G-invariant LCK metric. Suppose that U(1) acts on an LCK manifold M by …

We study the Fibered Isomorphism conjecture of Farrell and Jones for groups acting on trees. We show that under certain conditions the conjecture is true for groups acting on trees when the stabilizers satisfy the conjecture. These conditions are satisfied in several cases of the conjecture. We prove some general resul…

Loxodromic elements are pseudo-Anosov on specific graphs.

Groups act on Euclidean buildings with a minimum dimension bound.

This is a survey on old and new results as well as an introduction to various related basic notions and concepts, based on two talks given at the International Workshop on Geometry and Analysis in Kemerovo (Sobolev Institute of Mathematics, Kemerovo State University) and at the University of Krasnojarsk in June 2011. W…

Study shows solvable Lie groups act freely on compact pseudo-Riemannian manifolds.

It is proved that an arbitrary finite group acting locally linearly, homologically trivially, and pseudofreely on a closed, simply connected 4-manifold must in fact be cyclic and act semifreely, provided the second betti number of the manifold is at least three.

Infinite 2-groups of bounded exponent cannot act faithfully on compact manifolds.