Study of IR phases in 3D class R theories linked to non-hyperbolic 3-manifolds.
problem Understanding IR phases of 3D class R theories associated with non-hyperbolic 3-manifolds.
method Analysis of IR phenomena through `exceptional' Dehn fillings and gauging of flavor symmetries.
result 3D class R theories associated with certain atoroidal non-hyperbolic 3-manifolds exhibit supersymmetry enhancement at low energy.
Identifies 3D-index as invariant for cusped hyperbolic 3-manifolds.
problem Invariance of q-series for cusped hyperbolic 3-manifolds.
method Relates Frohman-Kania-Bartoszynska's q-series to Dimofte-Gaiotto-Gukov's 3D-index and tetrahedron index.
result Topological invariance of Frohman-Kania-Bartoszynska's q-series.
Study large N oscillations in 3D theories related to black hole physics.
problem Understanding large N sign oscillations in 3D theories via holography.
method Holographic computation of on-shell actions for Euclidean supergravity solutions, Wick rotation of magnetically charged AdS4 black holes.
result Proposed a non-trivial mathematical conjecture regarding phase factors of twisted Reidemeister-Ray-Singer torsion.
3D hyperbolic spaces have endless simple paths.
problem Finding simple paths in complex 3D spaces.
method Analyzing geodesics in hyperbolic 3-manifolds.
result Cusped hyperbolic 3-manifolds have infinitely many simple closed geodesics.
The paper classifies 3D contact partially hyperbolic diffeomorphisms.
problem Classifying contact partially hyperbolic diffeomorphisms in 3D.
method Smooth classification, conjugation to known flows or automorphisms, use of invariant distributions.
result Classification up to finite quotient or power, conjugation to known structures.
Uniform linear bounds on volume changes in 3D hyperbolic spaces.
problem Volume variation in hyperbolic 3-manifolds.
method Uniform linear bounds proof for drilling and filling operations.
result Uniform linear bounds on volume variation proved.
Paper finds new 3D shapes that can be inside a 4D space.
problem Finding new 3D shapes with specific properties.
method Examined arithmetic hyperbolic 3-manifolds and their homology.
result Discovered infinitely many 3D shapes that are rational homology spheres and can bound geometrically.
Study partially hyperbolic diffeomorphisms in 3D, focusing on foliations and dynamics.
problem Classify 3D partially hyperbolic diffeomorphisms homotopic to the identity.
method Analyze Burago and Ivanov's branching foliations in Seifert fibered and hyperbolic manifolds.
result Complete classification of diffeomorphisms in Seifert fibered manifolds, and new potential class in hyperbolic manifolds.
In this paper we will promote the 3D index of an ideal triangulation T of an oriented cusped 3-manifold M (a collection of q-series with integer coefficients, introduced by Dimofte-Gaiotto-Gukov) to a topological invariant of oriented cusped hyperbolic 3-manifolds. To achieve our goal we show that (a) T admits an index…
3D hyperbolic manifolds map one-to-one to their boundary character varieties.
problem Mapping 3D hyperbolic manifolds to their boundary character varieties.
method Using Bonahon-Schläfli formula and volume rigidity of discrete co-compact representations.
result Peripheral map is a birational isomorphism with its image.
Proves rigidity of 3D partially hyperbolic systems via autonomous dynamics.
problem Rigidity of partially hyperbolic diffeomorphisms in 3D.
method Introducing autonomous dynamical systems to prove rigidity.
result Rigidity of partially hyperbolic diffeomorphisms on 3-manifolds.
Defines a map connecting 3d-index and skein module.
problem Connecting mathematical physics predictions with topological quantum field theory.
method Defines a map from skein module to Laurent series ring.
result The map fulfills a supersymmetry prediction and is part of a conjectural topological quantum field theory.
New 3D shapes found without certain special flows.
problem Finding 3D shapes without specific special flows.
method Rational surgeries on the figure eight knot.
result First infinite family of hyperbolic 3-manifolds without tight projectively Anosov flows.
New 3D shapes found without certain flows.
problem Finding 3D shapes without specific flows.
method Using foliations and pseudo-Anosov flows, analyzing cusped hyperbolic 3-manifolds.
result First examples of 3D shapes without veering triangulations.
New surgeries found in 3D shapes without 2-spheres.
problem Finding non-hyperbolic surgeries in 3-manifolds.
method Combining work on hyperbolic knots and 3-manifolds with observations about surgeries.
result Every 3-manifold with certain properties contains a hyperbolic knot with a non-trivial surgery.
Explains research on 3D dynamics and manifold topology.
problem Understanding obstructions for Anosov flows on 3-manifolds.
method Expository note on partially hyperbolic diffeomorphisms and Anosov flows.
result Margulis and Plante-Thurston's topological obstructions for Anosov flows.
Study of 3d-3d correspondence involving q-Weyl algebra and 3d-index.
problem Understanding the action of a q-Weyl algebra on the 3d-index of knots. method Investigation of the q-Weyl algebra's module action on the 3d-index, conjecturing structural properties. result Bilinear factorization, pair of linear q-difference equations, and rational function matrix for the 3d-index determination. Classifies 3D partially hyperbolic systems, proving ergodicity.
problem Ergodicity of partially hyperbolic diffeomorphisms in 3-manifolds.
method Topological classification, Anosov flows, foliations, Gromov hyperbolicity.
result Complete answer to Hertz-Hertz-Ures conjecture for 3D systems.
Formula derived for ALH manifolds, showing existence of specific 3D manifolds.
problem Energy calculation and existence of specific 3D conformally compact ALH manifolds.
method Derivation of energy formula and application to manifold existence.
result Existence of 3D conformally compact ALH manifolds with specific properties.
Study connects flow dynamics to 3D geometry via surface intersections.
problem Relating flow dynamics to geometric properties of 3-manifolds.
method Relates pseudo-Anosov flow dynamics to hyperbolic geometry via curve graphs.
result Established a link between flow invariants and geometric features of 3-manifolds.
Study shows how to make 3D shapes hyperbolic with specific curves.
problem Understanding hyperbolic structures on 3-manifolds.
method Analyzing Heegaard splittings and using specific curves to prove hyperbolicity.
result Computed the length of a curve in terms of projection coefficients.
Paper shows 3D hyperbolic manifolds are uniquely identified by their finite groups.
problem Identifying hyperbolic 3-manifolds using their finite quotient groups.
method Proves profinite isomorphism of fundamental groups uniquely determines the manifold's isomorphism type.
result Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups.
Brunnian theta curves in 3D spheres have hyperbolic exteriors.
problem Characterizing Brunnian theta curves in 3D spheres.
method Sutured manifold theory, classification of annuli, and Thurston's hyperbolic geometry.
result Brunnian theta curves of low bridge number have hyperbolic exteriors with totally geodesic boundary.
One of the main challenges in 3d-3d correspondence is that no existent approach offers a complete description of 3d N=2 SCFT T[M3] --- or, rather, a "collection of SCFTs" as we refer to it in the paper --- for all types of 3-manifolds that include, for example, a 3-torus, Brieskorn spheres, and hyperbolic surgerie…
Corrected proof for 3D harmonic manifolds with minimal horospheres.
problem Proving 3D harmonic manifolds with minimal horospheres are either flat or hyperbolic.
method Provided a corrected proof for the classification of 3D harmonic manifolds.
result Classification of 3D harmonic manifolds: flat or hyperbolic.
The study characterizes constant curvature manifolds using ruled surfaces.
problem Characterizing manifolds of constant curvature using ruled surfaces.
method Investigating ruled surfaces in 3d Riemannian manifolds, finding stiction curve, distribution parameter, and fundamental forms.
result Identifies necessary and sufficient conditions for extrinsically flat surfaces to be ruled and proves manifold properties.
Paper finds infinite family of minimal triangulations for complex 3D shapes.
problem Finding minimal ideal triangulations for complex 3D shapes.
method Examined Dehn fillings on specific links to find minimal triangulations.
result Found an infinite family of minimal ideal triangulations for a specific type of 3D shape.
The study finds the maximum spectrum of 3D manifolds with lower scalar curvature.
problem Finding the maximum spectrum of 3D manifolds with lower scalar curvature.
method Establishing an analogous result to Cheng's theorem for 3D manifolds with scalar curvature lower bound.
result A splitting theorem for 3D manifolds with the maximal bottom spectrum.
"Ends of hyperbolic 3-manifolds should support canonical Wick Rotations, so they realize effective interactions of their ending globally hyperbolic spacetimes of constant curvature." We develop a consistent sector of WR-rescaling theory in 3D gravity, that, in particular, concretizes the above guess for many geometrica…
3D dual field theories for Virasoro minimal models constructed using Seifert fiber spaces.
problem Constructing 3D dual field theories for Virasoro minimal models.
method 3D-3D correspondence and Seifert fiber spaces.
result 3D dual field theories constructed for Virasoro minimal models.
A 3D space of hyperbolic manifolds is connected but not path-connected.
problem Proving connectivity and non-path-connectedness of framed hyperbolic 3-manifolds.
method Two proofs using density theorems for Kleinian groups, constructing dense sets of framings, and discussing paths.
result The space of framed infinite volume hyperbolic 3-manifolds is not path-connected.
New findings link 3D shapes to group properties.
problem Understanding groups with specific geometric properties.
method Analyzing spherical Plateau problems and 3-manifolds.
result Isometric solutions to Plateau problems imply geometric properties of groups.
We construct a new family of exact quantum field theories modeled on hyperbolic geometry, called {\it quantum hyperbolic field theories} (QHFTs). The QHFTs are defined for a (2+1)-bordism category based on the set of compact oriented 3-manifolds Y, equipped with properly embedded framed links $L_\Ff$ and with flat …
Researchers extend Chen, Erchenko, and Gogolev's result to more cases.
problem Embedding manifolds with hyperbolic geodesic trapped sets into compact manifolds with Anosov geodesic flows.
method Explains how assumptions can be removed to apply the result to all reasonable 3D examples.
result A broader applicability of the original result to all reasonable 3D examples.
We propose a new algorithm for Dehn surgery problem, finding exceptional Dehn filling slopes for a given hyperbolic 3-manifold with a torus boundary, using a quantum invariant called "3D index". The invariant is defined using an ideal triangulation of the cusped 3-manifold. We test the algorithm for many examples.
Study of higher spin Killing spinors on 3D manifolds, proving rigidity and providing explicit expressions.
problem Understanding higher spin Killing spinors on 3D manifolds.
method Definition and detailed study of higher spin Killing spinors in arbitrary dimension, focusing on 3D manifolds. Rigidity result and explicit expressions for 3-sphere and 3-hyperbolic space.
result Proved a rigidity result for 3D manifolds admitting higher spin Killing spinors and provided explicit expressions for these spinors.
We study supersymmetric probe M5-branes in the AdS_4 solution that arises from M5-branes wrapped on a hyperbolic 3-manifold M_3. This amounts to introducing internal defects within the framework of the 3d-3d correspondence. The BPS condition for a probe M5-brane extending along all of AdS_4 requires it to wrap a surfac…
Paper proves Luo's conjecture for 3D triangulated manifolds.
problem Finding hyperbolic metrics on compact 3-manifolds with boundary.
method Introduced and extended combinatorial Ricci flow to handle singularities.
result Proved Luo's conjecture affirmatively for ideal triangulations.
Proves helicity is the only regular Casimir for 3D hydrodynamics.
problem Identifying unique Casimir functions for 3D hydrodynamics.
method Normal forms, Poincaré-Birkhoff theorem, division lemma.
result Helicity is the only regular Casimir for volume-preserving diffeomorphisms.
We study 4d superconformal indices for a large class of N=1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T^2. An exchange of loops, which we call a "double Yang-Baxter move", gives the Seiberg duality of the gauge theory, and t…
Teichmüller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2,R) Chern-Simons theory. To physicists, it is known in particular in the context of 3d-3d correspondence and also in the holographic description of Virasoro conform…
Constructs hyperbolic reflection groups with 3D limit sets.
problem Existence of convex cocompact groups with specific limit sets.
method Inputting a simplicial complex into a construction process yields a hyperbolic reflection group.
result Answers Kapovich's question affirmatively by creating a thin subgroup of an arithmetic lattice.
Study gauged supergravity, M5-branes, and class R theories, constraining supergravity coefficients and calculating partition functions.
problem Constraints and calculations in higher-derivative supergravity and related theories.
method Holography, Chern-Simons theory, 3d-3d correspondence, wrapped M5-branes.
result Constrained coefficients in supergravity Lagrangian, calculated partition functions for class R theories.
Paper proves rigidity of metrics near hyperbolic ones in 3D.
problem Proving rigidity of metrics near hyperbolic ones in 3D.
method Introducing marked Poincaré determinant and proving local rigidity.
result Lichnerowicz Laplacian is injective in negative curvature.
New techniques solve Riccati equations on 3D manifolds, finding 4th order metric obstructions.
problem Solving Riccati-type equations with algebraic constraints on 3D Riemannian manifolds.
method Real algebraic geometry techniques, focusing on connection coefficients and Hessian equations.
result Obstruction to solving Riccati equations has order 4 in metric coefficients.
New algorithm constructs characters of rational VOAs from knot complements.
problem Constructing characters of rational VOAs from knot complements.
method 3D N=2 gauge theories, Dimofte-Gaiotto-Gukov construction, 3D N=4 rank-0 SCFT, topological twist. result New Nahm-sum-like expressions for Virasoro minimal model characters.
We show that the smooth geometry of a hyperbolic 3-manifold emerges from a classical spin system defined on a 2d discrete lattice, and moreover show that the process of this "dimensional oxidation" is equivalent with the dimensional reduction of a supersymmetric gauge theory from 4d to 3d. More concretely, we propose a…
The paper disproves a conjecture about 3D manifolds using even lattice points.
problem Thurston's Euler class one conjecture for fillable contact structures.
method Analyzing finite covers of hyperbolic 3-manifolds and properties of their dual Thurston norm unit balls.
result Found counter-examples to the conjecture using even lattice points on boundary.