arXiv research

Predicts morning traffic congestion using social media data from the previous evening.

Using publicly available traffic camera data in New York City, we quantify time-dependent patterns in aggregate pedestrian foot traffic. These patterns exhibit repeatable diurnal behaviors that differ for weekdays and weekends but are broadly consistent across neighborhoods in the borough of Manhattan. Weekday patterns…

We calculate realized volatility of the Nikkei Stock Average (Nikkei225) Index on the Tokyo Stock Exchange and investigate the return dynamics. To avoid the bias on the realized volatility from the non-trading hours issue we calculate realized volatility separately in the two trading sessions, i.e. morning and afternoo…

Study confirms USD/JPY rises at Gotobi days, suggesting trading strategy.

We analyze realized volatilities constructed using high-frequency stock data on the Tokyo Stock Exchange. In order to avoid non-trading hours issue in volatility calculations we define two realized volatilities calculated separately in the two trading sessions of the Tokyo Stock Exchange, i.e. morning and afternoon ses…

New algebraic structures on manifolds generalize supergeometry concepts.

Each element of the commutator subgroup of a group can be represented as a product of commutators. The minimal number of factors in such a product is called the commutator length of the element. The commutator length of a group is defined as the supremum of commutator lengths of elements of its commutator subgroup. We …

Doodles link to commutator identities in a 2-sphere.

Study on deformation cohomology for braided commutative structures.

Examining singularities of commuting vector fields on submanifolds.

Study on infinite-type surfaces shows stable commutator length is continuous and defines open subgroups.

New proof and description of commutator subgroups for free and surface groups.

Formulae for non-symmetric connections derived from covariant derivatives.

The paper studies Riemannian metrics on Lie groups with specific commutator subgroups.

Homotopy commutativity in quasitoric manifolds depends on polytope structure and characteristic matrix type.

Study introduces dynamical ideals for non-commutative rings and classifies knots and links.

Covariance is shown as a commutator in random variable calculus.

Every homeomorphism of Euclidean space is a commutator of two homeomorphisms.

We show that solutions of Thurston equation on triangulated 3-manifolds in a commutative ring carry topological information. We also introduce a homogeneous Thurston equation and a commutative ring associated to triangulated 3-manifolds.

We show that the mapping class group of any closed connected orientable surface of genus at least five is generated by only two commutators, and if the genus is three or four, by three commutators.

We give new upper bounds on the stable commutator lengths of Dehn twists in mapping class groups and new lower bounds on the stable commutator lengths of Dehn twists in hyperelliptic mapping class groups. In particular, we show that the stable commutator lengths of Dehn twists about a nonseparating and a separating cur…

Survey on invariant quasimorphisms and their relation to stable commutator length.

Paper proves non-compact inaudibility of symmetry and commutativity.

In this paper, we introduce a new commuting condition between the structure Jacobi operator and symmetric (1,1)-type tensor field $T$, that is, $R_ξφT=TR_ξφ$, where $T=A$ or $T=S$ for Hopf hypersurfaces in complex hyperbolic two-plane Grassmannians. By using simultaneous diagonalzation for commuting symmetric operators…

We introduce the notion of commuting Ricci tensor for real hypersurfaces in the complex quadric $Q^m = SO_{m+2}/SO_mSO_2$ . It is shown that the commuting Ricci tensor gives that the unit normal vector field $N$ becomes $\frak A$-principal or $\frak A$-isotropic. Then according to each case, we give a complete classifi…

The paper defines constraints for commuting endomorphisms in generalized tangent bundles.

Let $WB_n$ be the welded (or loop) braid group on n strands, $n \geq 3$. We investigate commutator subgroup of $WB_n$. We prove that the commutator subgroup $WB_n'$ is finitely generated and Hopfian. We show that $WB_n'$ is perfect if and only if $n \geq 5$. We also compute finite presentation for $FWB_n'$, the commuta…

An arbitrary homomorphism between groups is nonincreasing for stable commutator length, and there are infinitely many (injective) homomorphisms between free groups which strictly decrease the stable commutator length of some elements. However, we show in this paper that a random homomorphism between free groups is almo…

For any group, there is a natural (pseudo-)norm on the vector space B1 of real (group) 1-boundaries, called the stable commutator length norm. This norm is closely related to, and can be thought of as a relative version of, the Gromov (pseudo)-norm on (ordinary) homology. We show that for a free group, the unit ball of…

The paper finds commutator formulas for Gradient Ricci Shrinker metrics and applies them to linear stability.

The aim of this paper is to extend the notion of commutativity of vector fields to the category of singular foliations, using Nambu structures, i.e. integrable multi-vector fields. We will classify the relationship between singular foliations and Nambu structures, and show some basic results about commuting Nambu struc…

The quaternions are non-commutative. The deviation from commutativity is encapsulated in the commutator of unit quaternions. It is known that the k-th power of the commutator is null-homotopic if and only if k is divisible by 12. The main purpose of this paper is to construct a concrete null-homotopy of the 12-th power…

Study mixed commutator lengths in wreath products and their relation to general ranks.

Establishes a duality theorem connecting quasimorphisms and commutator lengths in group theory.

Reinterprets quantization commutes with reduction using KK-theory.

New framework for noncommutative Carrollian geometry using Lie-Rinehart pairs.

Study of Hermitian structures on Lie groups with 2D commutator subgroups.

We characterize Riemannian manifolds of constant sectional curvature in terms of commutation properties of their Jacobi operators.

Let $VB_n$, resp. $WB_n$ denote the virtual, resp. welded, braid group on $n$ strands. We study their commutator subgroups $VB_n' = [VB_n, VB_n]$ and, $WB_n' = [WB_n, WB_n]$ respectively. We obtain a set of generators and defining relations for these commutator subgroups. In particular, we prove that $VB_n'$ is finitel…

Study geometric structures and their interactions under different metrics.

Smooth structures on infinite dimensional Grassmannians and non-commutative cross-ratios.

The paper classifies Hopf hypersurfaces in complex quadrics with commuting Jacobi operators.

Given a fiber bundle $Z \to M \to B$ and a flat vector bundle $E \to M$ with a compatible action of a discrete group $G$, and regarding $B / G$ as the non-commutative space corresponding to the crossed product algebra, we construct an analytic torsion form as a non-commutative deRham differential form. We show that our…

Counting periodic geodesics of bounded length and commutator structure on hyperbolic surfaces.

We show that stable commutator length is rational on free products of free Abelian groups amalgamated over $\mathbb{Z}^k$, a class of groups containing the fundamental groups of all torus knot complements. We consider a geometric model for these groups and parameterize all surfaces with specified boundary mapping to th…

It is proved that the stable commutator length of a Dehn twist in the mapping class group is positive and the tenth power of a Dehn twist about a nonseparating simple closed curve is a product of two commutators. As an application a new proof of the fact that the growth rate of a Dehn twist is linear is given.

It is emphasized that equivalent definitions of connections on modules over commutative rings are not so in noncommutative geometry.

Uniform spectral gap found for stable commutator length in hyperbolic 2-orbifolds.