arXiv research

A method for making machine learning units-equivariant using dimensional analysis.

New minimal surfaces found in ball with boundary constraints.

Constructs a unique surface in a ball with specific properties.

Equivariant neural networks use symmetry to interpret complex data.

In this article we prove first of all the nonexistence of holomorphic submersions other than covering maps between compact quotients of complex unit balls, with a proof that works equally well in a more general equivariant setting. For a non-equidimensional surjective holomorphic map between compact ball quotients, our…

Two constructions of Chern character for equivariant vector bundles in noncommutative geometry.

Paper presents a novel neural network for MIMO symbol detection.

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

We prove that if M is a closed, connected, oriented, rationally inessential manifold, then the Hofer-Zehnder capacity of the unit disk bundle of the cotangent bundle of M is finite.

The paper extends toric variety correspondence to 4D almost complex torus manifolds.

We consider the equivariant Yamabe problem, i.e. the Yamabe problem on the space of G-invariant metrics for a compact Lie group G. The G-Yamabe invariant is analogously defined as the supremum of the constant scalar curvatures of unit volume G-invariant metrics minimizing the total scalar curvature functional in their …

Infinite $G$-invariant minimal hypersurfaces found in Riemannian manifolds.

Formula derived for Dirac operators on Lie groupoids.

We prove that every non-degenerate Reeb flow on a closed contact manifold $M$ admitting a strong symplectic filling $W$ with vanishing first Chern class carries at least two geometrically distinct closed orbits provided that the positive equivariant symplectic homology of $W$ satisfies a mild condition. Under further a…

The paper finds a special hypersurface in a manifold with positive Ricci curvature.

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…

Fixed points of mean section operators found in convex bodies.

The paper addresses selection bias in conformal prediction for focal units.

Consider the cyclic group C_2 of order two acting by complex-conjugation on the unit circle S^1. The main result is that a finitely dominated manifold W of dimension > 4 admits a cocompact, free, discontinuous action by the infinite dihedral group D_\infty if and only if W is the infinite cyclic cover of a free C_2-man…

New minimal hypersurfaces in 4D sphere found.

Analyzes convex structures in Teichmüller space unit tangent spheres.

Outer space and Teichmüller space fail well-rounded retract analogy.

We use our new type of bounded locally homeomorphic quasiregular mappings in the unit 3-ball to address long standing problems for such mappings. The construction of such mappings comes from our construction of non-trivial compact 4-dimensional cobordisms $M$ with symmetric boundary components and whose interiors have …

Maps asymptotically embed conic transforms from circle bundles.

A closed contact manifold is called Besse when all its Reeb orbits are closed, and Zoll when they have the same minimal period. In this paper, we provide a characterization of Besse contact forms for convex contact spheres and Riemannian unit tangent bundles in terms of $S^1$-equivariant spectral invariants. Furthermor…

We construct and analyze minimal disc stackings with bounds on their Morse index.

Study of a $G_2$-equivariant octonionic operator and its right spectrum.

As announced in [12], we develop a calculus of Fourier integral G-operators on any Lie groupoid G. For that purpose, we study convolability and invertibility of Lagrangian conic submanifolds of the symplectic groupoid T * G. We also identify those Lagrangian which correspond to equivariant families parametrized by the …

A new geometric perceptron model improves 3D shape classification.

In this paper we present the construction of explicit quasi-isomorphisms that compute the cyclic homology and periodic cyclic homology of crossed-product algebras associated with (discrete) group actions. In the first part we deal with algebraic crossed-products associated with group actions on unital algebras over any…

In statistical analysis, measuring a score of predictive performance is an important task. In many scientific fields, appropriate scores were tailored to tackle the problems at hand. A proper score is a popular tool to obtain statistically consistent forecasts. Furthermore, a mathematical characterization of the proper…

Let $\mathcal{O}(D)$ be an equivariant line bundle which is big and nef on a complex projective nonsingular toric variety $X$. Given a continuous toric metric $\|\cdot\|$ on $\mathcal{O}(D)$, we define the energy at equilibrium of $(X,φ_{\bar{D}})$ where $φ_{\bar{D}}$ is the weight of the metrized toric divisor $\bar{D…

We prove hyperbolic 3-manifolds are geometrically inflexible: a unit quasiconformal deformation of a Kleinian group extends to an equivariant bi-Lipschitz diffeomorphism between quotients whose pointwise bi-Lipschitz constant decays exponentially in the distance form the boundary of the convex core for points in the th…

Study of invariants on manifolds with boundary involving equivariant spectral flow and η-invariants.

Group-equivariant subsampling layers improve CNNs' equivariance.

Study of equivariant ribbon concordance using Khovanov homology.

Defines a new homomorphism for strongly invertible knots, proving equivariant algebraic concordance.

We show Péter Csorba's conjecture that the graph homomorphism complex Hom(C_5,K_{n+2}) is homeomorphic to a Stiefel manifold, the space of unit tangent vectors to the n-dimensional sphere. For this a general tool is developed that allows to replace the complexes Hom(G, K_n) by smaller complexes that are homeomorphic to…

Defines an equivariant Ruelle dynamical zeta function for flows on manifolds.

Study of equivariant movie moves for involutive links.

We define the equivariant holonomy of an invariant connection on a principal U(1)-bundle. The properties of the ordinary holonomy are generalized to the equivariant setting. In particular, equivariant U(1)-bundles with connection are shown to be classified by its equivariant holonomy modulo isomorphisms. We also show t…

A bound on knot unknotting using equivariant signature.

New proof for 4D symplectic manifolds: equivariant cohomology determines diffeotype.

The paper develops methods for calculating equivariant homology from Morse functions.

Efficiently samples and learns densities with symmetries using equivariant methods.

Study shows non-equivariant and equivariant non-orientable 4-genus of periodic knots can differ.

In this paper, we establish an infinitesimal equivariant index formula in the noncommutative geometry framework using Greiner's approach to heat kernel asymptotics. An infinitesimal equivariant index formula for odd dimensional manifolds is also given. We define infinitesimal equivariant eta cochains, prove their regul…

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