arXiv research

New lattices from 4-manifolds show manifold properties.

Hybrid subgroups found in non-arithmetic PU(2,1) lattices.

New non-arithmetic lattice found in PU(3,1)

New property identifies arithmetic lattices from nonuniform lattices.

New lattice stick knot condition identified.

Simplified proof for lattice link projections.

This work compares lattice-free and lattice-based training criteria for LVCSR.

Research finds bounds for knots in hexagonal lattice and classifies 11-stick knots.

We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term distributive homology and show some of its properties. The main result is a complete formula for the homology o…

Course on arithmetic lattices at EPFL.

Upper bound for lattice stick number of spatial graphs.

New thin subgroups found in special linear groups via bending techniques.

New rigidity theorem for product of lattices.

This paper studies the covolumes of nonuniform arithmetic lattices in PU(n, 1). We determine the smallest covolume nonuniform arithmetic lattices for each n, the number of minimal covolume lattices for each n, and study the growth of the minimal covolume as n varies. In particular, there is a unique lattice (up to conj…

The paper finds incommensurable lattices in complex models of Baumslag-Solitar groups.

Proves a lattice version of the Atiyah-Singer index theorem.

Vertex distortion measures how far lattice knots deviate from straight lines.

Regular integer lattices are characterized by k unit vectors that build up their generator matrices. These have rank k for D-lattices, and are rank-deficient for A-lattices, for E_6 and E_7. We count lattice points inside hypercubes centered at the origin for all three types, as if classified by maximum infinity norm i…

The paper proves residual finiteness of certain lattices and constructs surfaces with specific fundamental groups.

Proves properties of arithmetic lattices and hyperbolic manifolds.

A celebrated theorem of Hadwiger states that the Euler-Poincaré characteristic is the the unique invariant and continuous valuation on the distributive lattice of compact polyhedra in R^n that assigns value one to each convex non-empty such polyhedron. This paper provides an analogue of Hadwiger's result for finitely p…

The cubic lattice stick index of a knot type is the least number of sticks necessary to construct the knot type in the 3-dimensional cubic lattice. We present the cubic lattice stick index of various knots and links, including all (p,p+1)-torus knots, and show how composing and taking satellites can be used to obtain t…

New method finds lattice polygons that can be dissected into triangles with integer areas.

Hybrid lattices produce subgroups of PU(n,1) from PU(n-1,1) lattices.

L-CNNs approximate gauge actions, revealing fixed points with no lattice artifacts.

The paper refines transformations of lattice diagrams and introduces dotted diagrams.

Classifies knots by lattice size, finding unknot ratios and crossing numbers.

Let $G$ be a simply connected, solvable Lie group and $Γ$ a lattice in $G$. The deformation space $\mathcal{D}(Γ,G)$ is the orbit space associated to the action of $\Aut(G)$ on the space $\mathcal{X}(Γ,G)$ of all lattice embeddings of $Γ$ into $G$. Our main result generalises the classical rigidity theorems of Mal'tsev…

Proves effective slope gaps for lattice surfaces.

Improved lattice field theory simulations with local-Autoregressive Conditional Normalizing Flow.

Study answers arithmeticity question for normal subgroup of lattices.

Study investigates lattices fibring over the circle, focusing on BNSR invariants.

One type of switch simplifies operations on lattice knots.

New lattices in higher dimensions have dense surface subgroups.

Defines and analyzes the holonomy Lie algebra of geometric lattices.

A new surgery formula for knot lattice homology.

We construct an infinite commutative lattice of groups whose dual spaces give Kauffman finite-type invariants of long virtual knots. The lattice is based "horizontally" upon the Polyak algebra and extended "vertically" using Manturov's functorial map $f$. For each $n$, the $n$-th vertical line in the lattice contains a…

The (isothermic) compressibility of lattice knots can be examined as a model of the effects of topology and geometry on the compressibility of ring polymers. In this paper, the compressibility of minimal length lattice knots in the simple cubic, face centered cubic and body centered cubic lattices are determined. Our r…

Researchers reinterpret complex hyperbolic orbifolds using line arrangements.

The study examines knot probabilities in confined lattice polygons.

New research shows certain arithmetic lattices can't be LERF.

New lattice path method for statistical inference of persistent diagrams.

The paper classifies a specific type of hyperbolic lattices using geometric properties.

The study finds surface subgroups in cocompact lattices of $H^{2n}$ for $n\geq2$.

The study connects lattices, Garside structures, and weakly modular graphs.

Researchers create a fundamental domain for all Deligne-Mostow lattices in PU(2,1).

Study uses instanton Floer theory to find definite lattices from certain 4-manifolds.

Improved speech recognition for voice assistants by analyzing speech data.