arXiv research

Aspherical configuration Lie groupoids complement is proven for a class of orbifolds.

Proves conjecture on graph configuration spaces' complexity.

Study of circle configurations in the plane, proving aspherical space and computing fundamental groups.

The paper proves asphericity of configuration spaces and covers them with entire functions.

Surveying topological complexity of graph configurations, unifying traditional and modern approaches.

A 2-manifold's group structure is deduced from orbit configuration spaces.

The paper studies fundamental groups of orbit configuration spaces and proves their torsion-freeness.

The n-string braid group of a graph X is defined as the fundamental group of the n-point configuration space of the space X. This configuration space is a finite dimensional aspherical space. A. Abrams and R. Ghrist have conjectured that this braid group is a right angled Artin group if X is planar. We prove their conj…

The paper extends a fibration theorem to all orbifolds, proving an isomorphism conjecture.

Paper confirms Whitehead's conjecture for aspherical 2-complexes.

This paper contains examples of closed aspherical manifolds obtained as a by-product of recent work by the author [arXiv:math.GR/0509490] on the relative strict hyperbolization of polyhedra. The following is proved. (I) Any closed aspherical triangulated n-manifold M^n with hyperbolic fundamental group is a retract of …

Study a relative aspherical conjecture and prove 3-manifold obstruction to positive scalar curvature.

Relative notions of combinatorial asphericity have been used to prove that injective labeled oriented trees (which encode spines of ribbon 2-knots) are aspherical. This article presents an overview and comparison of the different notions of relative combinatorial asphericity. It also contains new results concerning cha…

The paper proves the Singer conjecture for aspherical complex surfaces and refines Gromov's inequality.

Constructs 4-manifolds with positive Euler characteristic proving a conjecture.

Study new bounds on TC of spaces with subgroup inclusions.

We prove that every finitely generated group with recursive aspherical presentation embeds into a group with finite aspherical presentation. This and several known facts about groups and manifolds imply that there exists a 4-dimensional closed aspherical manifold $M$ such that the fundamental group $π_1(M)$ coarsely co…

The study of $PD_3$-pairs extends results for aspherical 3-manifolds.

Study finite group actions on aspherical manifolds, proving rigidity and symmetry bounds.

Nilpotent Sasakian manifolds are Heisenberg nilmanifolds.

This is a survey article on symplectically aspherical manifolds. The paper contains a discussion on constructions of symplectically aspherical manifolds, their topological properties and the role of this class in symplectic topology. Research perspectives are discussed.

3D spaces without boundaries are found that aren't manifolds.

The paper extends a vanishing theorem for hypersurfaces in aspherical manifolds.

A {\em word labeled oriented graph} (WLOG) is an oriented graph $\cal G$ on vertices $X=\{ x_1,\ldots ,x_k\}$, where each oriented edge is labeled by a word in $X^{\pm1}$. WLOGs give rise to presentations which generalize Wirtinger presentations of knots. WLOG presentations, where the underlying graph is a tree are of …

The "polyhedral product functor" produces a space from a simplicial complex L and a collection of pairs of spaces, {(A(i),B(i))}, where i ranges over the vertex set of L. We give necessary and sufficient conditions for the resulting space to be aspherical. There are two similar constructions, each of which starts with …

Study shows some complex shapes don't fit a certain property.

Study aspherical manifolds with boundaries, proving homological criteria.

Study symplectically aspherical Kähler manifolds with unique properties.

We establish isosystolic inequalities for a class of manifolds which includes the aspherical manifolds. In particular, we relate the systolic volume of aspherical manifolds first to their minimal entropy, then to the algebraic entropy of their fundamental groups.

Researchers propose a new approach to the Hopf problem for aspherical varieties.

A labeled oriented tree is called injective if each generator occurs at most once as an edge label. We show that injective labeled oriented trees are aspherical. The proof relies on a new relative asphericity test based on a lemma of Stallings.

Diagrammatic reducibility DR and its generalization vertex asphericity VA are combinatorial tools developed for detecting asphericity of a 2-complex. Here we present tests for a relative version of VA that apply to pairs of 2-complexes $(L,K)$, where $K$ is a subcomplex of $L$. We show that a relative weight test holds…

The paper describes the structure of injective LOT-complexes and proves they are aspherical.

Aspherical manifolds with bounded curvature have non-trivial abelian subgroups in their fundamental groups.

We provide upper bounds on the size of the homology of a closed aspherical Riemannian manifold that only depend on the systole and the volume of balls. Further, we show that linear growth of mod p Betti numbers or exponential growth of torsion homology imply that a closed aspherical manifold is "large".

Let $G/H$ be a contractible homogeneous Sasaki manifold. A compact locally homogeneous aspherical Sasaki manifold $Γ\big\backslash G/H$ is by definition a quotient of $G/H$ by a discrete uniform subgroup $Γ\leq G$. We show that a compact locally homogeneous aspherical Sasaki manifold is always quasi-regular, that is, $…

This paper studies limits of aspherical manifolds with specific curvature conditions.

Using small cancellation for rotating families of groups, we construct new examples of aspherical polyhedra.

We define a new class of irreducible groups, called groups not infinite-index presentable by products or not IIPP. We prove that certain aspherical manifolds with fundamental groups not IIPP do not admit maps of non-zero degree from direct products. This extends previous results of Kotschick and Loeh, providing new cla…

Every compact aspherical Riemannian manifold admits a canonical series of orbibundle structures with infrasolv fibers which is called its infrasolv tower. The tower arises from the solvable radicals of isometry group actions on the universal covers. Its length and the geometry of its base measure the degree of continuo…

This is a survey on known results and open problems about closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. Many examples come from certain kinds of non-positive curvature conditions. The property aspherical which is a purely homotopy theoretical condition implies…

The study shows that certain cubical presentations lead to aspherical spaces.

New groups derived from square configurations have right-angled and HNN structures.

Let $U$ be an arbitrary word in letters $x_1^{\pm 1}, ..., x_m^{\pm 1}$ and $m \ge 2$. We prove that the group presentation $<x_1, ..., x_m \|\ U x_i U^{-1} = x_{i+1}, i=1,..., m-1>$ is aspherical. The proof is based upon prior partial results of A. Klyachko and the author on the asphericity of such presentations.

We show that the aspherical manifolds produced via the relative strict hyperbolization of polyhedra enjoy many group-theoretic and topological properties of open finite volume negatively pinched manifolds, including relative hyperbolicity, nonvanishing of simplicial volume, co-Hopf property, finiteness of outer automor…

In this note we present examples of $K(π,1)$-arrangements which admit a restriction which fails to be $K(π,1)$. This shows that asphericity is not hereditary among hyperplane arrangements.

The paper explores automorphism groups of parabolic structures on aspherical manifolds.

In this paper, Problem 4.17 on R. Kirby's problem list is solved by constructing infinitely many aspherical 4-manifolds that are homology 4-spheres