arXiv research

The study characterizes and verifies equivariant embeddings of symmetric Kählerian manifolds.

Constructs equivariant embeddings of Hermitian symmetric spaces into tangent spaces.

We consider a compact connected CR manifold with a transversal CR locally free $\mathbb R$-action endowed with a rigid positive CR line bundle. We prove that a certain weighted Fourier-Szegő kernel of the CR sections in the high tensor powers admits a full asymptotic expansion and we establish $\mathbb R$-equivariant K…

Study on embedding surfaces into 3-manifolds, focusing on equivariant cases.

Minimal dimensions found for flag manifolds embeddings.

In 1993, Bismut and Zhang establish a mod Z embedding formula of Atiyah-Patodi-Singer reduced eta invariants. In this paper, we explain the hidden mod Z term as a spectral flow and extend this embedding formula to the equivariant family case. In this case, the spectral flow is generalized to the equivariant chern chara…

Minimal equivariant embedding found for flag manifolds.

The paper provides bounds for embedding manifolds into Euclidean spaces with group actions.

This paper proves the existence of a smooth embedding for symmetrical manifolds.

Minimal sphere dimension for equivariant embedding of circles.

EbC learns equivariant embeddings from unlabeled group actions.

Let $X$ be a compact strongly pseudoconvex CR manifold with a transversal CR $S^1$-action. In this paper, we establish the asymptotic expansion of Szegő kernels of positive Fourier components and by using the asymptotics, we show that $X$ can be equivariant CR embedded into some $\mathbb C^N$ equipped with a simple $S^…

Classifies linear embeddings of grassmannians and ind-grassmannians.

We compute the homotopy type of the space of T^n-equivariant symplectic embeddings from the standard 2n-dimensional ball of some fixed radius into a 2n-dimensional symplectic-toric manifold M, and use this computation to define a Z-valued step function on the positive real line which is an invariant of the symplectic-t…

This work proposes a geometric approach to equivariant message passing on Riemannian manifolds.

By computing certain cohomology of Vect(M) of smooth vector fields we prove that on 1-dimensional manifolds M there is no quantization map intertwining the action of non-projective embeddings of the Lie algebra sl(2) into the Lie algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant quantization ex…

New tool: relative Hopf invariant for Poincaré surgery.

We present a deformation for constant mean curvature tori in the 3-sphere. We show that the moduli space of equivariant constant mean curvature tori in the 3-sphere is connected, and we classify the minimal, the embedded, and the Alexandrov embedded tori therein. We conclude with an instability result.

We consider a compact CR manifold with a transversal CR locally free circle action endowed with a rigid positive CR line bundle. We prove that a certain weighted Fourier-Szegő kernel of the CR sections in the high tensor powers admits a full asymptotic expansion. As a consequence, we establish an equivariant Kodaira em…

Given two Fuchsian representations $ρ_l$ and $ρ_r$ of the fundamental group of a closed oriented surface $S$ of genus $\geq 2$, we study the relation between Lagrangian submanifolds of $M_ρ=(\mathbb{H}^2/ρ_l(π_1(S)))\times (\mathbb{H}^2/ρ_r(π_1(S)))$ and $ρ$-equivariant embeddings $σ$ of $\widetilde S$ into Anti-de Sit…

Our work improves VAE latent space clustering by enforcing invariant and equivariant learning.

Study of equivariant movie moves for involutive links.

New minimal discs and annuli found in ellipsoids.

The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle projections. Roughly speaking, a normally non-singular map is a map together with such a …

This work introduces a method for almost equivariance in neural networks using Lie algebra convolutions.

Geodesic surfaces embed into hyperbolic 3-manifolds for all finite group actions.

The study finds many Möbius bands and annuli on toroids.

Minimal dimensions for Riemann surface embeddings computed for specific groups.

Paper generalizes spectral flow formulas for compact Lie group actions.

We generalise theorems of Khodorovskiy and Park-Park-Shin, and give new topological proofs of those theorems, using embedded surfaces in the 4-ball and branched double covers. These theorems exhibit smooth codimension-zero embeddings of certain rational homology balls bounded by lens spaces.

For an orbifold, there is a notion of an orbifold embedding, which is more general than the one of sub-orbifolds. We develop several properties of orbifold embeddings. In the case of translation groupoids, we show that such a notion is equivalent to a strong equivariant immersion.

In this paper, a classification of free involutions on 3-dimensional homotopy complex projective spaces is given. By the $\mathbb Z_2$-equivariant Montgomery-Yang correspondence, we obtain all smooth involutions on $S^6$ with fixed-point set an embedded $S^3$.

New constraints on embedded spheres and projective planes in 4-manifolds from Seiberg-Witten theory.

Develops equivariant Seiberg-Witten-Floer cohomology for 3-spheres.

The paper generalizes free boundary min-max theory to equivariant settings.

The paper classifies equivariant test configurations for spherical varieties.

New spaces help connect manifold structures on equivariant Poincaré spaces.

We study isometric actions of tree automorphism groups on the infinite-dimensional hyperbolic spaces. On the one hand, we exhibit a general one-parameter family of such representations and analyse the corresponding equivariant embeddings of the trees, showing that they are convex-cocompact and asymptotically isometric.…

Paper presents a novel hyperbolic neural network for efficient data representation.

The paper proves an adjunction inequality for Real embedded surfaces in 4-manifolds.

Equivariant trisections for group actions on 4-manifolds are introduced and studied.

Let G --> G' be an embedding of semisimple complex Lie groups, let B and B' be a pair of nested Borel subgroups, and let f:G/B --> G'/B' be the associated equivariant embedding of flag manifolds. We study the pullbacks of cohomologies of invertible sheaves on G'/B' along the embedding f. Let O' be a G'-equivariant inve…

New minimal hypersurfaces in 4D sphere found.

New minimal hypersphere found in 4-sphere solving Bernstein problem.

The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In this work, we pay attention to scale changes, which regularly appear in various t…

IsoGCNs learn invariant and equivariant graph features for efficient simulations.

The paper generalizes equivariant neural networks on homogeneous spaces to the non-linear setting.

Rotationally equivariant convolutions improve molecular property prediction.