arXiv research

We study fundamental groups of toroidal compactifications of non compact ball quotients and show that the Shafarevich conjecture on holomorphic convexity for these complex projective manifolds is satisfied in dimension 2 provided the corresponding lattice is arithmetic and small enough. The method is to show that the A…

A closed 4-manifold (or, more generally, a finite $PD_4$-space) has a finitely dominated infinite regular covering space if and only if either its universal covering space is finitely dominated or it is finitely covered by the mapping torus of a self homotopy equivalence of a $PD_3$-complex.

Study covers of Chamanara surface with large Veech groups.

The paper characterizes geometrically finite surfaces via geodesic covers.

New orbifolds found that cover manifolds but not in a finite way.

Study covers of sphere with homeomorphisms lifting property.

Study shows no new eigenvalues in specific finite coverings.

This paper studies isotopies of periodic tangles in 3-manifolds using finite covers.

Bayesian methods often misinterpret data and asymptotic concepts.

Anabelian geometry reformulated using Hodge theory for hyperbolic curves.

Develops methods for dynamic pricing in incomplete data settings.

We present a method for deciding when a regular abelian cover of a finite CW-complex has finite Betti numbers. To start with, we describe a natural parameter space for all regular covers of a finite CW-complex X, with group of deck transformations a fixed abelian group A, which in the case of free abelian covers of ran…

The study finds a limit on subgroup complexity in hyperbolic 3-manifold groups.

Lower bounds for cover degrees of hyperbolic 3-manifolds.

We provide the twisted Alexander polynomials of finite abelian covers over three-dimensional manifolds whose boundary is a finite union of tori. This is a generalization of a well-known formula for the usual Alexander polynomial of knots in finite cyclic branched covers over the three-dimensional sphere.

3-manifolds are chiral if not finitely covered by sphere or product.

Finite vector bundles over complex manifolds are trivializable via finite covers.

Tangle machines are a topologically inspired diagrammatic formalism to describe information flow in networks. This paper begins with an expository account of tangle machines motivated by the problem of describing `covariance intersection' fusion of Gaussian estimators in networks. It then gives two examples in which ta…

Odd covers have one Anosov flow, even covers have two.

The paper finds new graph covers with exceptionally low degree.

Open manifolds can be covered by $\mathbb{R}^m$ with finite or infinite degree.

An orbifold is a Morita equivalence class of a proper {\' e}tale Lie groupoid. A unitary equivalence class of spectral triples over the algebra of smooth invariant functions are associated with any compact spin orbifold. In the case of an effective spin orbifold we construct a collection of spectral triples over the sm…

We identify branched coverings (continuous open surjections p:Y->X of Hausdorff spaces with uniformly bounded number of pre-images) with Hilbert C*-modules C(Y) over C(X) and with faithful unital positive conditional expectations E:C(Y)->C(X) topologically of index-finite type. The case of non-branched coverings corres…

Tiny complexes share 3-5 triangles in common coverings.

Study bottom of spectra on orbifolds via coverings.

We prove the homotopy invariance of L^2 torsion for covering spaces, whenever the covering transformation group is either residually finite or amenable. In the case when the covering transformation group is residually finite and when the L^2 cohomology of the covering space vanishes, the homotopy invariance was establi…

The paper proves every closed curve on a bouquet of circles lifts to finite covers.

The paper proves conditions for self-covering manifolds to be fiber bundles over a circle.

Theory of $H$-graded manifolds and coverings of supermanifolds.

Characterizes compact complex surfaces with finite homotopy rank-sum.

Integration of the form $\int_a^\infty {f(x)w(x)dx}$, where $w(x)$ is either $\sin (ω{\kern 1pt} x)$ or $\cos (ω{\kern 1pt} x)$, is widely encountered in many engineering and scientific applications, such as those involving Fourier or Laplace transforms. Often such integrals are approximated by a numerical integration…

Minimal example found for two finite CW-complexes sharing a common covering.

We show that the commutator subgroup G' of a classical knot group G need not have subgroups of every finite index, but it will if G' has a surjective homomorphism to the integers and we give an exact criterion for that to happen. We also give an example of a smoothly knotted n-sphere in the (n+2)-sphere for all n at le…

Homology of surface coverings solved for genus 3 and above.

We prove that any two finite-area non-compact hyperbolic Riemann surfaces S and T have finite covers that are arbitrarily close in the normalized Weil-Petersson metric, where we normalize by dividing the square of the metric by the area of the surface. In the case where T is the modular surface this reduces to showing …

We provide related Dehn surgery descriptions for rational homology spheres and a class of their regular finite cyclic covering spaces. As an application, we use the surgery descriptions to relate the Casson invariants of the covering spaces to that of the base space. Finally, we show that this places restrictions on th…

We prove that if $M \longrightarrow P$ is a small cover of a compact right-angled hyperbolic polyhedron $P$ then $M$ admits a cofinal tower of finite sheeted covers with positive rank gradient. As a corollary, if $π_1(M)$ is commensurable with the reflection group of $P$, then $M$ admits a cofinal tower of finite sheet…

The existence of essential closed surfaces surfaces is proven for finite coverings of 3-manifolds that are triangulated by finitely many topological ideal tetrahedra and admit a regular, negatively curved, ideal structure.

Study shows how to embed any group into the first homology of a 3-manifold cover.

Two complexes share a common covering but not a finite one.

The paper studies random covers of torus knot complements and their statistical properties.

Conditions for simple closed curves in surface covers.

Simple lifts of non-simple curves on surfaces.

Hempel has shown that the fundamental groups of knot complements are residually finite. This implies that every nontrivial knot must have a finite-sheeted, noncyclic cover. We give an explicit bound, $Φ(c)$, such that if $K$ is a nontrivial knot in the three-sphere with a diagram with $c$ crossings and a particularly s…

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

We give an upper bound for the growth of homology torsions of finite coverings of irreducible 3-manifolds with tori boundary in terms of hyperbolic volume.

Let S be an orientable surface with negative Euler characteristic, let ψ\in\Mod(S) be a mapping class of S, and let T_ψ be the mapping torus of ψ. We study the action of lifts of ψon the homology of finite covers of S via the torsion homology growth of towers of finite covers of T_ψ. We show that ψadmits a lift to a fi…

Given a sub-hyperbolic semi-rational branched covering which is not CLH-equivalent a rational map, it must have the non-empty canonical Thurston obstruction. By using this canonical Thurston obstruction, we decompose this dynamical system in this paper into several sub-dynamical systems. Each of these sub-dynamical sys…