arXiv research

Study irrational pencils on complex manifolds, finding non-finitely generated homology.

We investigate the coarse homology of leaves in foliations of compact manifolds. This is motivated by the observation that the non-leaves constructed by Schweitzer and by Zeghib all have non-finitely generated coarse homology. This led us to ask whether the coarse homology of leaves in a compact manifold always has to …

We amend the statement of point~(i) in Theorem~1.3 in arxiv:0901.1022 and supply the additional arguments and minor changes for the results that depend on it. We also seize the occasion and generalize to non-finitely generated lattices.

We give a short proof of a theorem of Handel and Mosher stating that any finitely generated subgroup of $\text{Out}(F_N)$ either contains a fully irreducible automorphism, or virtually fixes the conjugacy class of a proper free factor of $F_N$, and we extend their result to non finitely generated subgroups of $\text{Ou…

Paper detects non-trivial cycles in embedding spaces using graph integrals.

In this note we consider the relationship between the dressing action and the holonomy representation in the context of constant mean curvature surfaces. We characterize dressing elements that preserve the topology of a surface and discuss dressing by simple factors as a means of adding bubbles to a class of non finite…

In geometric group theory one uses group actions on spaces to gain information about groups. One natural space to use is the Cayley graph of a group. The Cayley graph arguments that one encounters tend to require local finiteness, and hence finite generation of the group. In this paper, I take the theory of intersectio…

In this paper it is proven that if the group of covering translations of the covering space of a compact, connected, $P^2$-irreducible 3-manifold corresponding to a non-trivial, finitely-generated subgroup of its fundamental group is infinite, then either the covering space is almost compact or the subgroup is infinite…

Study of cluster and skein algebras for surfaces, showing their connection.

Study mapping class groups of 4-manifolds, proving non-finitely generated and splitting properties.

The study solves a 2008 problem by Kalai about infinitely many homology-spheres.

Classification of groups as symmetries of infinite translation surfaces.

New method constructs non-quasiconvex subgroups in hyperbolic groups.

We classify the 3-dimensional hyperbolic polyhedral orbifolds that contain no embedded essential 2-suborbifolds, up to decomposition along embedded hyperbolic triangle orbifolds (turnovers). We give a necessary condition for a 3-dimensional hyperbolic polyhedral orbifold to contain an immersed (singular) hyperbolic tur…

The paper consists of two parts. In the first one we show that a relatively hyperbolic group $G$ splits as a star graph of groups whose central vertex group is finitely generated and the other vertex groups are maximal parabolic subgroups. As a corollary we obtain that every group which admits 3-discontinuous and 2-coc…

Study of special Kato manifolds derived from toric geometry.

We give lower bounds for the growth of the number of Reeb chords and for the volume growth of Reeb flows on spherizations over closed manifolds M that are not of finite type, have virtually polycyclic fundamental group, and satisfy a mild assumption on the homology of the based loop space. For the special case of geode…

Smooth resolutions found for quotient of R^2 by infinite discrete groups.

Constructs 3D topological field theories from a specific quantum group, linking to physics invariants.

GPry accelerates Bayesian inference for non-Gaussian posteriors.

The bundle approach and n-contextuality reveal quantum model contextuality.

Paper defines generalized braids and proves their subgroup status.

Defines a new Poisson structure for generalized Sasakian spaces.

Improved image generation through iterative flow matching to reduce hallucinations.

Framework generates personalized insulin treatment strategies using deep models.

OptiGAN uses GAN and RL to optimize sequence generation for specific goals.

Survey on deep models for graph generation.

Improves deep generative models to generate images of any size.

Develops a unified theory of Yang-Mills and GR using generalized principal bundles.

Meta-CoTGAN improves adversarial text generation by preventing mode collapse.

Generative models can still learn from contaminated data, but with limitations.

Generative AI tasks analyzed for text, images, audio, video, code, and molecules.

Defines Kahler angle for a broader context.

Established a generalized Boothby-Wang theorem in contact geometry.

The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry à la Hitchin). The generalized twistor space associated to such a manifold is defined as the bundle of generalized complex structures on the tangent spaces of the…

We present a characterization, in terms of torsion-free generalized connections, for the integrability of various generalized structures (generalized almost complex structures, generalized almost hypercomplex structures, generalized almost Hermitian structures and generalized almost hyper-Hermitian structures) defined …

This research proves guarantees on sequence models' generalization to longer and novel sequences.

SHADOWCAST generates graphs with user-specified attributes.

In this paper we define the notion of a generalized coKähler structure and prove that the product $M_{1}\times M_{2}$ of generalized contact metric manifolds $(M_i, Φ_i,E_{\pm,i}, G_i)$, $i=1, 2$, where $M_{1}\times M_{2}$ is endowed with the product generalized complex structure induced from $Φ_1$ and $Φ_2$, is gener…

We define the generalized connected sum for generic closed plane curves, generalizing the strange sum defined by Arnold, and completely describe how the Arnold invariants $J^{\pm}$ and $\mathit{St}$ behave under the generalized connected sums.

In this communication, we describe some interrelations between generalized $q$-entropies and a generalized version of Fisher information. In information theory, the de Bruijn identity links the Fisher information and the derivative of the entropy. We show that this identity can be extended to generalized versions of en…

A new method generates graphs with hierarchical structures.

The paper extends symplectic techniques to generalized complex geometry.

We study the problem of generating interesting endings for stories. Neural generative models have shown promising results for various text generation problems. Sequence to Sequence (Seq2Seq) models are typically trained to generate a single output sequence for a given input sequence. However, in the context of a story,…

A new method for generating sets and graphs without requiring exchangeability.

DeepWeightFlow generates diverse neural network weights efficiently.

Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of generalized functions we define the notions of generalized pseudo-Riemannian met…

It is known that the scalar curvature arises as the moment map in Kahler geometry. In pursuit of this analogy, we introduce the notion of a moment map in generalized Kahler geometry which gives the definition of a generalized scalar curvature on a generalized Kahler manifold. From the viewpoint of the moment map, we ob…