A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper proves infinitely many strong symplectic fillings for cusp singularity links.
The paper explores cusp types in hyperbolic 4-manifolds and their commensurability classes.
We determine the number of cusps of minimal Picard modular surfaces. The proof also counts cusps of other Picard modular surfaces of arithmetic interest. Consequently, for each N > 0 there are finitely many commensurability classes of nonuniform arithmetic lattices in SU(2, 1) that contain an N-cusped surface. We also …
The study finds arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps.
3-manifolds have covers with infinitely many ideal triangulations.
Study reveals uniform spectral gaps for random hyperbolic surfaces with few cusps.
Study on random hyperbolic surfaces with many cusps, focusing on tight geodesics.
3D hyperbolic spaces have endless simple paths.
New hyperbolic 3-manifolds with multiple cusps are found that sound the same but look different.
A horospherical torus about a cusp of a hyperbolic manifold inherits a Euclidean similarity structure, called a cusp shape. We bound the change in cusp shape when the hyperbolic structure of the manifold is deformed via cone deformation preserving the cusp. The bounds are in terms of the change in structure in a neighb…
For a single cusped hyperbolic 3-manifold, Hodgson proved that there are only finitely many Dehn fillings of it whose trace fields have bounded degree. In this paper, we conjecture the same for manifolds with more cusps, and give the first positive results in this direction. For example, in the 2-cusped case, if a mani…
This paper considers "geometric" ideal triangulations of cusped hyperbolic 3-manifolds, i.e. decompositions into positive volume ideal hyperbolic tetrahedra. We exhibit infinitely many geometric ideal triangulations of the figure eight knot complement. As far as we know, this is the first construction of infinitely man…
We construct infinitely many examples of pairs of isospectral but non-isometric -cusped hyperbolic -manifolds. These examples have infinite discrete spectrum and the same Eisenstein series. Our constructions are based on an application of Sunada's method in the cusped setting, and so in addition our pairs are fin…
We show that the set of cusp shapes of hyperbolic tunnel number one manifolds is dense in the Teichmuller space of the torus. A similar result holds for tunnel number n manifolds. As a consequence, for fixed n, there are infinitely many hyperbolic tunnel number n manifolds with at most one exceptional Dehn filling. Thi…
This study of properly or strictly convex real projective manifolds introduces notions of parabolic, horosphere and cusp. Results include a Margulis lemma and in the strictly convex case a thick-thin decomposition. Finite volume cusps are shown to be projectively equivalent to cusps of hyperbolic manifolds. This is pro…
We classify all the non-hyperbolic Dehn fillings of the complement of the chain-link with 3 components, conjectured to be the smallest hyperbolic 3-manifold with 3 cusps. We deduce the classification of all non-hyperbolic Dehn fillings of infinitely many 1-cusped and 2-cusped hyperbolic manifolds, including most of tho…
We prove a Hitchin-Thorpe inequality for noncompact Einstein 4-manifolds with asymptotic geometry at infinity. The asymptotic geometry at infinity is either a cusp bundle over a compact space (the fibered cusps) or a fiber bundle over a cone with a compact fiber (the fibered boundary). Many noncompact Einstein manifold…
Proves existence and uniqueness of metrics with negative curvature and singularities on compact surfaces.
In this note, we show that there exist cusped hyperbolic -manifolds that embed geodesically, but cannot bound geometrically. Thus, being a geometric boundary is a non-trivial property for such manifolds. Our result complements the work by Long and Reid on geometric boundaries of compact hyperbolic -manifolds, and…
The study provides polynomial bounds for essential surfaces in various 3-manifolds.
We show that there are at most finitely many one cusped orientable hyperbolic 3-manifolds which have more than eight non-hyperbolic Dehn fillings. Moreover, we show that determining these finitely many manifolds is decidable.
It has been observed that most manifolds in the Callahan-Hildebrand-Weeks census of cusped hyperbolic -manifolds are obtained by surgery on the minimally twisted 5-chain link. A full classification of the exceptional surgeries on the 5-chain link has recently been completed. In this article, we provide a complete cl…
We consider the existence of simple closed geodesics or "geodesic knots" in finite volume orientable hyperbolic 3-manifolds. Previous results show that at least one geodesic knot always exists [Bull. London Math. Soc. 31(1) (1999) 81-86], and that certain arithmetic manifolds contain infinitely many geodesic knots [J. …
It is experimentally known that achiral hyperbolic 3-manifolds are quite sporadic at least among those with small volume, while we can find plenty of them as amphicheiral knot complements in the 3-sphere. In this paper, we show that there exist infinitely many achiral 1-cusped hyperbolic 3-manifolds not homeomorphic to…
Profinite rigidity of certain 3-manifolds detected through Dehn fillings.
It is shown that with finitely many exceptions, the fundamental group obtained by Dehn surgery on a one cusped hyperbolic 3-manifold contains the fundamental group of a closed surface.
New noncompact Coxeter polytopes found in various dimensions.
Y. Benoist proved that if a closed three-manifold M admits an indecomposable convex real projective structure, then M is topologically the union along tori and Klein bottles of finitely many sub-manifolds each of which admits a complete finite volume hyperbolic structure on its interior. We describe some initial result…
Study describes frequencies of geodesics on hyperbolic surfaces as genus grows.
4-manifolds show every flat 3-manifold as cusp sections.
In this paper we deepen the analysis of certain classes M_{g,k} of hyperbolic 3-manifolds that were introduced in a previous work by B. Martelli, C. Petronio and the author. Each element of M_{g,k} is an oriented complete finite-volume hyperbolic 3-manifold with compact connected geodesic boundary of genus g and k cusp…
Characterizes holonomies of convex projective cusps.
Study geodesics entering a fixed cusp neighborhood multiple times.
We find that cusp densities of hyperbolic knots in the 3-sphere are dense in [0,0.6826...] and those of links are dense in [0,0.853...]. We define a new invariant associated with cusp volume, the cusp crossing density, as the ratio between the cusp volume and the crossing number of a link, and show that cusp crossing d…
To a hyperbolic manifold one can associate a canonical projective structure and ask whether it can be deformed or not. In a cusped manifold, one can ask about the existence of deformations that are trivial on the boundary. We prove that if the canonical projective structure of a cusped manifold is infinitesimally proje…
The paper classifies different types of cusps on plane curves.
The paper characterizes links in 3D from divides with cusps.
Given a compact orientable surface with finitely many punctures , let $\Cal S(Σ)$ be the set of isotopy classes of essential unoriented simple closed curves in . We determine a complete set of relations for a function from $\Cal S(Σ)$ to to be the geodesic length function of a hyperbolic metric with geo…
We classify the orientable finite-volume hyperbolic 3-manifolds having non-empty compact totally geodesic boundary and admitting an ideal triangulation with at most four tetrahedra. We also compute the volume of all such manifolds, we describe their canonical Kojima decomposition, and we discuss manifolds having cusps.…
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.
Veech groups uniformize Teichmüller geodesic curves in Riemann moduli space. Recently, examples of infinitely generated Veech groups have been given. We show that these can even have infinitely many cusps and infinitely many infinite ends. We further show that examples exist for which each direction of an infinite end …
Let Y be a noncompact rank one locally symmetric space of finite volume. Then Y has a finite number e(Y) > 0 of topological ends. In this paper, we show that for any natural number n, the Y with e(Y) \leq n that are arithmetic fall into finitely many commensurability classes. In particular, there is a constant c_n such…
The paper classifies cusp types in hyperbolic knot complements.
New findings on cusped Borel Anosov representations and their properties.
Study of parabolic-preserving deformations of hyperbolic lattices.
Study of large- asymptotics for Weil-Petersson volumes of hyperbolic surfaces with cusps.
We apply a spherical CR Dehn surgery theorem in order to obtain infinitely many Dehn surgeries of the Whitehead link complement that carry spherical CR structures. We consider as starting point the spherical CR uniformization of the Whitehead link complement constructed by Parker and Will, using a Ford domain in the co…
Study on singularities of Lagrangian immersions with applications in Floer theory.