1,720,969 research outputs found
A cusped hyperbolic 4-manifold without spin structures
Full text linkWe build a non-compact, orientable, hyperbolic four-manifold of finite volume that does not admit any spin structure
New hyperbolic 4–manifolds of low volume
No full textWe prove that there are at least two commensurability classes of (cusped, arithmetic)
minimal-volume hyperbolic 4–manifolds. Moreover, by applying a well-known
technique due to Gromov and Piatetski-Shapiro, we build the smallest known non-
arithmetic hyperbolic 4–manifold
Convex plumbings in closed hyperbolic 4-manifolds
No full textWe show that every plumbing of disc bundles over surfaces whose genera satisfy a simple inequality may be embedded as a convex submanifold in some closed hyperbolic four-manifold. In particular its interior has a geometrically finite hyperbolic structure that covers a closed hyperbolic four-manifold
Embedding non-arithmetic hyperbolic manifolds
Full text linkThis paper shows that many hyperbolic manifolds obtained by glueing
arithmetic pieces embed into higher-dimensional hyperbolic manifolds as
codimension-one totally geodesic submanifolds. As a consequence, many
Gromov--Pyatetski-Shapiro and Agol--Belolipetsky--Thomson non-arithmetic
manifolds embed geodesically. Moreover, we show that the number of
commensurability classes of hyperbolic manifolds with a representative of
volume that bounds geometrically is at least , for large
enough.Comment: 20 pages, 5 figures. Final versio
Character varieties of a transitioning Coxeter 4-orbifold
Full text linkInternational audienceIn 2010, Kerckhoff and Storm discovered a path of hyperbolic 4-polytopes eventually collapsing to an ideal right-angled cuboctahedron. This is expressed by a deformation of the inclusion of a discrete reflection group (a right-angled Coxeter group) in the isometry group of hyperbolic 4-space. More recently, we have shown that the path of polytopes can be extended to Anti-de Sitter geometry so as to have geometric transition on a naturally associated 4-orbifold, via a transitional half-pipe structure. In this paper, we study the hyperbolic, Anti-de Sitter, and half-pipe character varieties of Kerckhoff and Storm's right-angled Coxeter group near each of the found holonomy representations, including a description of the singularity that appears at the collapse. An essential tool is the study of some rigidity properties of right-angled cusp groups in dimension four
Geometric transition from hyperbolic to Anti-de Sitter structures in dimension four
Full text linkInternational audienceWe provide the first examples of geometric transition from hyperbolic to Anti-de Sitter structures in dimension four, in a fashion similar to Danciger's three-dimensional examples. The main ingredient is a deformation of hyperbolic 4-polytopes, discovered by Kerckhoff and Storm, eventually collapsing to a 3-dimensional ideal cuboc-tahedron. We show the existence of a similar family of collapsing Anti-de Sitter polytopes, and join the two deformations by means of an opportune half-pipe orbifold structure. The desired examples of geometric transition are then obtained by gluing copies of the polytope
Hyperbolic Dehn filling in dimension four
Full text linkWe introduce and study some deformations of complete finite-volume hyperbolic four-manifolds that may be interpreted as four-dimensional analogues of Thurston’s hyperbolic Dehn filling. We construct in particular an analytic path of complete, finite-volume cone four-manifolds Mtthat interpolates between two hyperbolic four-manifolds M0and M1with the same volume 8/3π2. The deformation looks like the familiar hyperbolic Dehn filling paths that occur in dimension three, where the cone angle of a core simple closed geodesic varies monotonically from 0 to 2π. Here, the singularity of Mt is an immersed geodesic surface whose cone angles also vary monotonically from 0 to 2π. When a cone angle tends to 0 a small core surface (a torus or Klein bottle) is drilled, producing a new cusp. We show that various instances of hyperbolic Dehn fillings may arise, including one case where a degeneration occurs when the cone angles tend to 2π, like in the famous figure-eight knot complement example. The construction makes an essential use of a family of four-dimensional deforming hyperbolic polytopes recently discovered by Kerckhoff and Storm
Spines of minimal length
Full text linkIn this paper we raise the question whether every closed Riemannian manifold has a spine of minimal area, and we answer it affirmatively in the surface case. On constant curvature surfaces we introduce the spine systole, a continuous real function on moduli space that measures the minimal length of a spine in each surface. We show that the spine systole is a proper function and has its global minima precisely on the extremal surfaces (those containing the biggest possible discs).
We also study minimal spines, which are critical points for the length functional. We completely classify minimal spines on flat tori, proving that the number of them is a proper function on moduli space. We also show that the number of minimal spines of uniformly bounded length is finite on hyperbolic surfaces
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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