A closed 4-manifold (or, more generally, a finite -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 -complex.
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48 results for “finite covers”
Study covers of Chamanara surface with large Veech groups.
problem Characterize finite abelian covers with large Veech groups.
method Analyze Veech groups of finite abelian covers of the Chamanara surface.
result Every free group arises as the projective Veech group of a finite-area infinite translation surface.
The paper characterizes geometrically finite surfaces via geodesic covers.
problem Characterizing geometrically finite surfaces.
method Study of geodesic covers of Fuchsian groups and their metric properties.
result Finiteness of geodesic covers characterizes geometrically finiteness.
New orbifolds found that cover manifolds but not in a finite way.
problem Finding orbifolds that cover manifolds but not finitely.
method Constructing specific orbifolds.
result Examples of orbifolds that cover manifolds but not finitely.
Study covers of sphere with homeomorphisms lifting property.
problem Finite abelian covers of sphere with lifting homeomorphisms.
method Completely determined covers with specific lifting property.
result Properties of finite abelian covers with lifting homeomorphisms.
Study shows no new eigenvalues in specific finite coverings.
problem Proving the absence of new eigenvalues in finite coverings.
method Analyzing spectral stability of finite coverings with specific conditions on Ricci curvature and representation theory.
result Non-existence of new eigenvalues in a specific range.
This paper studies isotopies of periodic tangles in 3-manifolds using finite covers.
problem Understanding equivalence relations of periodic tangles in 3-manifolds.
method Employing techniques from 3-manifold topology to study complements of links.
result Isotopies between different finite covers of isotopic links are preserved.
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.
problem Understanding subgroups of bounded rank in hyperbolic 3-manifold groups.
method Proving a finiteness theorem for subgroups of bounded rank.
result Every bounded rank covering tower of closed hyperbolic 3-manifolds is a tower of finite covers associated to a fibration over a 1-orbifold.
Lower bounds for cover degrees of hyperbolic 3-manifolds.
problem Finding lower bounds for cover degrees of hyperbolic 3-manifolds.
method Using volume, diameter, and new invariants to establish lower bounds.
result Established lower bounds for cover degrees in terms of given parameters.
The twisted Alexander polynomial for finite abelian covers over three manifolds with boundarymath.GT
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.
problem Characterizing chiral 3-manifolds.
method Analyzing finite covers and self-homeomorphisms.
result Prime 3-manifolds not finitely covered by sphere or product are chiral.
Finite vector bundles over complex manifolds are trivializable via finite covers.
problem Understanding when holomorphic vector bundles over compact complex manifolds are trivializable.
method Introducing finite bundles and using finite étale covers to trivialize holomorphic vector bundles.
result Holomorphic vector bundles over compact complex manifolds are finite if and only if they admit a flat holomorphic connection with finite monodromy.
Odd covers have one Anosov flow, even covers have two.
problem Classifying Anosov flows on 3-manifolds with specific covers.
method Analyzing finite covers of geodesic flows on 3-manifolds.
result Odd covers result in one Anosov flow class, even covers in two.
The paper finds new graph covers with exceptionally low degree.
problem Graph covers with primitive homology not spanned by lifts.
method Focused on finite -group deck groups, developed a character table-based algorithm.
result Found the smallest known nontrivial examples with covering degree 128.
Open manifolds can be covered by with finite or infinite degree.
problem Covering open manifolds with .
method Proving simple branched covers for open manifolds of dimensions 2 and 3, and investigating universal bases.
result Open manifolds can be covered by with finite or infinite degree.
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 non-Leighton complexesmath.GT
Tiny complexes share 3-5 triangles in common coverings.
problem Complexes sharing common coverings with finite triangles.
method Pseudo-simplicial triangulation analysis.
result Minimum triangles in common coverings are 3, 4, or 5.
Study bottom of spectra on orbifolds via coverings.
problem Behavior of bottom of spectra under orbifold coverings.
method Analysis of scalar Schrödinger operators on orbifolds.
result Results apply to geometrically finite and conformally compact orbifolds.
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.
problem Proving closed curves lift to finite covers of free groups.
method Explicitly constructing families of l-sheeted normal coverings and characterizing lifts.
result 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.
problem Conditions for self-covering manifolds to be fiber bundles over a circle.
method Developed a criterion for finite generation of modules over a commutative Noetherian ring and proved conditions for fiber bundles.
result Proved that certain self-covering manifolds with free abelian fundamental group are fiber bundles over a circle.
-covering of a supermanifoldmath.DG
Theory of -graded manifolds and coverings of supermanifolds.
problem Developing a theory for -graded manifolds and coverings of supermanifolds.
method Using tools from representation theory, we introduce and investigate -graded coverings of supermanifolds.
result Theory of -graded coverings of supermanifolds introduced and investigated.
Characterizes compact complex surfaces with finite homotopy rank-sum.
problem Compact complex surfaces with finite homotopy rank-sum.
method Characterization and proof of Steinness of universal cover.
result Smooth compact complex Kaehler surfaces with finite homotopy rank-sum.
Minimal example found for two finite CW-complexes sharing a common covering.
problem Finding the minimum number of 2-cells in two finite CW-complexes that share a common covering.
method Constructing an almost minimal example with two 2-cells in each complex.
result Minimal example with two 2-cells in each complex.
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.
problem Homology of finite coverings of a surface.
method Proved rational homology group generated by specific cycles.
result For , rational homology group is generated by cycles in a specific subsurface.
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 …
A Dehn surgery description of regular finite cyclic covering spaces of rational homology spheresmath.GT
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 is a small cover of a compact right-angled hyperbolic polyhedron then admits a cofinal tower of finite sheeted covers with positive rank gradient. As a corollary, if is commensurable with the reflection group of , then 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.
problem Embedding finite abelian groups into the first homology of 3-manifold covers.
method Proves existence of finite covers with prescribed torsion.
result Any finite abelian group can be a direct factor in the first homology of a 3-manifold cover.
Two complexes share a common covering but not a finite one.
problem Common covering of complexes with specific properties.
method Constructing CW-complexes K and L with a common covering.
result K is homeomorphic to a complex with a single 2-cell.
The paper studies random covers of torus knot complements and their statistical properties.
problem Understanding the statistical behavior of finite covers of torus knot complements.
method Asymptotic subgroup growth analysis and Benjamini-Schramm limit theorems.
result Determination of the linear growth rate of Betti numbers for random covers of torus knot complements.
Conditions for simple closed curves in surface covers.
problem Conditions for simple closed curves in surface covers.
method Necessary and sufficient conditions for integral homology classes.
result Conditions for existence of simple closed curves in covers.
Simple lifts of non-simple curves on surfaces.
problem Finding simple lifts of non-simple closed curves on surfaces.
method Constructing finite covers and curves on surfaces.
result Explicit non-simple closed curves with simple lifts on degree n covers.
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, , such that if is a nontrivial knot in the three-sphere with a diagram with crossings and a particularly s…
The paper proves residual finiteness of certain lattices and constructs surfaces with specific fundamental groups.
problem Residual finiteness of lattices in and existence of smooth projective surfaces.
method Proved residual finiteness of certain lattices and constructed surfaces using central extensions.
result First examples of residually finite lattices in and construction of 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.
Homological eigenvalues of mapping classes and torsion homology growth for fibered 3--manifoldsmath.GR
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…
Torus covers have controlled volume and diameter under curvature and diameter bounds.
problem Bounding volume and diameter of torus covers with curvature and diameter constraints.
method Using lower Ricci curvature bound and upper diameter bound, constructing finite-sheeted covering spaces.
result Recovering and extending a result of Kloeckner and Sabourau with controlled bounds.
Generalizes Leighton's theorem to cube complexes.
problem Extending graph covering theorem to cube complexes.
method Generalizes Leighton's theorem to a family of cube complexes.
result Cube complexes have common finite covers.
Uniform waist inequalities proven for manifolds with Kazhdan groups in codimension two.
problem Proving uniform waist inequalities for manifolds with specific group properties.
method Using finite covers and Cheeger inequality for manifolds with Kazhdan fundamental groups.
result Finite covers of manifolds with Kazhdan groups satisfy uniform waist inequalities in codimension two.
An inverse limit of a sequence of covering spaces over a given space is not, in general, a covering space over but is still a lifting space, i.e. a Hurewicz fibration with unique path lifting property. Of particular interest are inverse limits of finite coverings (resp. finite regular coverings), which yield fi…
Develops algorithm for finite generating set of liftable mapping class groups of regular abelian covers.
problem Finding finite generating sets for liftable mapping class groups of regular abelian covers.
method Algorithm based on a result providing generating sets for groups acting on graphs with finite quotients.
result Provides finite generating sets for for various regular abelian covers.
Random branched covers of groups are homotopy equivalent to geometrically small cancellation complexes.
problem Understanding the topological properties of random branched covers of groups.
method Constructing a random model for branched covers and showing asymptotic homotopy equivalence to geometrically small cancellation complexes.
result The fundamental group of a random branched cover is Gromov hyperbolic and has small cohomological dimension.
We are interested in finite groups acting orientation-preservingly on 3-manifolds (arbitrary actions, ie not necessarily free actions). In particular we consider finite groups which contain an involution with nonempty connected fixed point set. This condition is satisfied by the isometry group of any hyperbolic cyclic …