Proves strong Tits alternative for 3D automorphisms over zero char fields.
problem Tits alternative for 3D tame automorphisms over zero char fields.
method Proved strong Tits alternative using 3D tame automorphisms over zero char fields.
result Strong Tits alternative proven for 3D tame automorphisms over zero char fields.
Classifies 3D manifolds with specific structures and automorphisms.
problem Classifying compact 3D manifolds with path structures and large automorphism groups.
method Uses Cartan connections and constant curvature analysis.
result Curvature of Cartan connections is constant for these manifolds.
The paper classifies isometries on specific Lie groups.
problem Classifying isometries on nonnilpotent, solvable 3D Lie groups.
method Proving automorphisms are the only isometries for rank two Almost-Riemannian Structures.
result A classification result for rank two ARSs on nonnilpotent, solvable 3D Lie groups.
The paper classifies path structures on 3D Lie groups and reduces non-flat ones to Z/2Z-structures.
problem Classifying and reducing path structures on 3D Lie groups.
method Analyzes curvature and automorphism groups to reduce path structures to simpler forms.
result Automorphism groups of non-flat path structures are maximal dimension 3.
The paper classifies 3D spherical Sasakian manifolds using geometric and algebraic methods.
problem Classifying 3D spherical Sasakian manifolds with specific properties.
method Establishing correspondence between different sets of parameters and geometrically describing the moduli space.
result Determination of Sasakian automorphism groups and detection of homogeneous Sasakian manifolds.
The abstract discusses resurgent functions in quantum knot invariants.
problem Understanding the asymptotic expansion of quantum knot invariants.
method Using resurgent functions and q-series to conjecture and compute knot invariants. result Explicit computations match conjectured values for specific knots.
Study of symmetries in 3D Lie groups, determining index and moduli space properties.
problem Understanding symmetries in 3D Lie groups and their moduli space.
method Computed full isometry groups of left-invariant metrics on 3D Lie groups.
result Determined index of symmetry and properties of moduli space.
Complex Chern-Simons theory reveals peacock patterns in perturbative series.
problem Understanding the structure of partition functions in complex Chern-Simons theory.
method Analyzing the partition function as a holomorphic function and using resurgence theory.
result Perturbative series are resurgent, with trans-series involving non-perturbative variables.
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.
Smoothly conjugate Anosov flows on 3D manifolds are actually smoothly conjugate.
problem Smoothly conjugate 3D Anosov flows are not always smoothly conjugate.
method Proved smooth rigidity for volume preserving Anosov flows on 3-manifolds.
result Smooth conjugacy implies smooth conjugacy for volume preserving Anosov flows.
This paper identifies all topological symmetry groups for Heawood family graphs.
problem Understanding symmetries of spatial graphs in 3D space.
method Analyzing automorphisms of graphs embedded in S3. result All graphs in the Heawood family are intrinsically chiral.
This paper classifies topological symmetry groups for Petersen family graphs.
problem Understanding symmetries of graphs embedded in 3D space.
method Examined all embeddings of Petersen family graphs in S3 and classified their topological symmetry groups. result Identified all possible groups that can be realized as topological symmetry groups for each graph in the Petersen family.
Study classifies special metrics for which the isometry group of 3D Lie groups is larger than expected.
problem Classifying metrics for which the isometry group of 3D Lie groups is larger than expected.
method Lie-theoretical methods to classify pairs (G, g)
result Determines the dimension of the isometry group for every pair (G, g)
Study left invariant Lorentzian metrics on 3D non-unimodular Lie groups.
problem Classify and analyze left invariant Lorentzian metrics on 3D non-unimodular Lie groups.
method Classify metrics up to automorphism, study curvature functions.
result Obtain Ricci operator, scalar curvature, and sectional curvatures as functions of metrics.
Automorphisms of handlebodies arise naturally in the a classification of automorphisms of three-manifolds. Among automorphisms of handlebodies, there are certain automorphisms called irreducible (or generic), which are analogues of pseudo-Anosov automorphisms of surfaces. We show that irreducible automorphisms of handl…
We study knots in 3d Chern-Simons theory with complex gauge group SL(N,C), in the context of its relation with 3d N=2 theory (the so-called 3d-3d correspondence). The defect has either co-dimension 2 or co-dimension 4 inside the 6d (2,0) theory, which is compactified on a 3-manifold M^. …
Study shows RAAG automorphisms and outer automorphisms are not relatively hyperbolic.
problem Characterizing automorphism and outer automorphism groups of RAAGs.
method Analyzing groups of RAAGs with at least 3 vertices, categorizing based on graph structure.
result Automorphism and outer automorphism groups of RAAGs are not relatively hyperbolic.
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. Study knot invariants using automorphism groups of free nilpotent groups.
problem Developing knot invariants using automorphism groups.
method Nilpotently p-localization of knot groups and automorphism groups of free nilpotent groups. result Maps from outer automorphism groups yield knot invariants.
Constructs Cartan geometries from automorphism behaviors.
problem Determining Cartan geometries from automorphism local behavior.
method Introduces a construction for Cartan geometries capturing automorphism local behavior.
result The sprawl uniquely characterizes Cartan geometries with equivalent local behavior.
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.
In this paper, we investigate the structure of the automorphism groups of pure braid groups. We prove that, for n>3, $\Aut(P_n)$ is generated by the subgroup $\Aut_c(P_n)$ of central automorphisms of Pn, the subgroup $\Aut(B_n)$ of restrictions of automorphisms of Bn on Pn and one extra automorphism wn. W…
3D flying wings created for any angle asymptotic cones.
problem Creating 3D steady gradient Ricci solitons with any angle asymptotic cones.
method Constructing 3D flying wings for any angle asymptotic cones.
result 3D flying wings constructed for any angle asymptotic cones.
Automorphism groups of Hopf manifolds are finite and have a bounded order.
problem Understanding the structure of automorphism groups of Hopf manifolds.
method Proved that the automorphism groups of Hopf manifolds are Jordan.
result Automorphism groups of Hopf manifolds are finite and have a bounded order.
Automorphisms of pants complex are shown to be inner.
problem Understanding automorphisms of pants complexes.
method Proving automorphisms are inner for specific groups.
result Automorphism groups are naturally isomorphic to pants complex.
Proposes a new effective central charge for 3d N=2 theories.
problem Understanding the effective central charge in 3d N=2 theories.
method Analyzes the superconformal index to propose a new quantity and discusses its properties and computation.
result Proposes a new effective central charge for 3d N=2 theories.
Autonomous driving requires 3D perception of vehicles and other objects in the in environment. Much of the current methods support 2D vehicle detection. This paper proposes a flexible pipeline to adopt any 2D detection network and fuse it with a 3D point cloud to generate 3D information with minimum changes of the 2D d…
Smooth 3D flows from non-smooth starting points.
problem Creating smooth Ricci flows from non-smooth initial conditions.
method Generalized singular Ricci flow applied to 3D complete manifolds.
result Existence of smooth Ricci flows starting from non-smooth initial conditions.
3D Axial-Attention improves lung nodule classification accuracy.
problem Limited 3D attention in existing methods.
method Proposes 3D Axial-Attention network with 3D positional encoding.
result 3D Axial-Attention achieves state-of-the-art performance.
Classifies and constructs all extendable automorphisms of closed surfaces over the 3-sphere.
problem Identifying extendable automorphisms of closed surfaces over the 3-sphere.
method Classification and construction of extendable automorphisms through embeddings and Heegaard surfaces.
result All extendable automorphisms of closed surfaces can be induced by automorphisms of the 3-sphere on Heegaard surfaces.
Finite groups can be automorphism groups of translation surfaces with poles.
problem Existence of finite automorphism groups on translation surfaces with poles.
method Analyzing translation surfaces with poles and extending results to branched projective structures.
result Finite groups can be automorphism groups of translation surfaces with poles.
3D steady gradient Ricci solitons are all O(2)-symmetric.
problem Characterizing 3D steady gradient Ricci solitons.
method Analyzing asymptotic behavior and using O(2) symmetry.
result All 3D steady gradient Ricci solitons are O(2)-symmetric.
DreamFusion uses text-to-image diffusion models to create 3D images efficiently.
problem Lack of large-scale 3D datasets and efficient architectures for 3D synthesis.
method Adapting a 2D diffusion model to 3D synthesis using a loss based on probability density distillation.
result A 3D model can be optimized from a 2D diffusion model, allowing for text-to-3D synthesis.
Automorphisms of Lie algebras and their root systems are fully lifted.
problem Understanding automorphisms of real semisimple Lie algebras and their root systems.
method Proving every automorphism of the restricted root system can be lifted to a Lie algebra automorphism.
result Automorphisms of restricted root systems can be fully lifted to Lie algebras.
Parabolic automorphisms on hyperkahler manifolds act ergodically on fibers.
problem Understanding the dynamics of parabolic automorphisms on hyperkahler manifolds.
method Analyzing the action of parabolic automorphisms on the second cohomology group and fibers of Lagrangian fibrations.
result Parabolic automorphisms preserving Lagrangian fibrations act ergodically on the fibers.
3D Convolutional Neural Networks (3D-CNN) have been used for object recognition based on the voxelized shape of an object. However, interpreting the decision making process of these 3D-CNNs is still an infeasible task. In this paper, we present a unique 3D-CNN based Gradient-weighted Class Activation Mapping method (3D…
Deep generative architectures provide a way to model not only images but also complex, 3-dimensional objects, such as point clouds. In this work, we present a novel method to obtain meaningful representations of 3D shapes that can be used for challenging tasks including 3D points generation, reconstruction, compression…
Free groups' automorphisms have bounded orbits.
problem Understanding automorphisms of infinite rank free groups.
method Proved coarsely bounded automorphism groups via metric space actions.
result Free groups' automorphism groups have quasi-isometry type of a point.
Study growth rates of automorphisms of special groups.
problem Understanding the growth rates of automorphisms of special groups.
method Analyzing outer automorphisms of virtually special groups, showing polynomial or exponential growth, and constructing Nielsen-Thurston decompositions.
result Outer automorphism groups of virtually special groups are boundary amenable, have finite virtual cohomological dimension, and satisfy the Tits alternative.
Study on automorphisms of K3 and Enriques surfaces, proving entropy gaps and achirality.
problem Entropy norms and achirality of automorphisms on K3 and Enriques surfaces.
method Proves gap theorems for entropy norms and studies achirality in terms of genus-one fibrations.
result Entropy gaps and achirality results for automorphisms of K3 and Enriques surfaces.
Research examines octonionic slice regular functions and their automorphisms and invariants.
problem Analyzing slice regular functions in the octonionic algebra.
method Investigates automorphisms and invariants of octonionic slice regular functions.
result Characterizes the automorphisms and invariants of octonionic slice regular functions.
We consider automorphisms of homogeneous parabolic geometries with a fixed point. Parabolic geometries carry the distinguished distributions and we study those automorphisms which enjoy natural actions on the distributions at the fixed points. We describe the sets of such automorphisms on homogeneous parabolic geometri…
Study finds conditions for finite-dimensional Lie group structure in basic automorphism groups of certain Cartan foliations.
problem Characterizing the basic automorphism groups of Cartan foliations.
method Analyzes sufficient conditions and estimates dimensions for basic automorphism groups of Cartan foliations covered by fibrations.
result Identifies sufficient conditions for the existence of a finite-dimensional Lie group structure in basic automorphism groups.
Classifies hyperbolic manifolds with specific automorphism groups.
problem Classifying Kobayashi-hyperbolic manifolds with high-dimensional automorphism groups.
method Analyzes manifolds of dimension n≥2 with automorphism groups of dimensions n2−7 or n2−8. result Completes the classification for automorphism groups n2−7 and n2−8. Outer automorphism groups of Coxeter groups are trivial except for small ranks.
problem Triviality of outer automorphism groups of Coxeter groups.
method Using Guirardel-Levitt outer space for free products, proving triviality and cyclic order for specific ranks.
result Outer automorphism groups are trivial except for small ranks.
Paper describes invariants of slice regular functions' automorphism group.
problem Understanding invariants of slice regular functions' automorphism group.
method Analyzes automorphism group of slice regular functions over Clifford algebras.
result Describes invariants of the automorphism group of slice regular functions.
We classify isotopy classes of automorphisms (self-homeomorphisms) of 3-manifolds satisfying the Thurston Geometrization Conjecture. The classification is similar to the classification of automorphisms of surfaces developed by Nielsen and Thurston, except an automorphism of a reducible manifold must first be written as…
Graph Neural Networks improve 3D object detection in LiDAR point clouds.
problem Challenges in processing LiDAR data due to its 3D geometry and massive volume.
method Proposes a Graph Neural Network (GNN) based framework for 3D object detection.
result GNNs successfully identify objects in 3D LiDAR point clouds.