arXiv research

Geometrically characterizes binary sextics with a vanishing quadratic invariant.

To determine the Lie groups that admit a flat (eventually complete) left invariant semi-Riemannian metric is an open and difficult problem. The main aim of this paper is the study of the flatness of left invariant semi Riemannian metrics on quadratic Lie groups i.e. Lie groups endowed with a bi-invariant semi Riemannia…

Study centers of mapping-torus groups to define knot and mapping class invariants.

Study identifies specific subvarieties in translation surfaces with quadratic field.

This paper shows how to create quadratic differentials with any given singularities.

The paper extends arithmetic Chern-Simons invariants to real quadratic fields and calculates mod 2 Dijkgraaf-Witten invariants.

We call a metric $m$-quasi-Einstein if $Ric_X^m$ (a modification of the $m$-Bakry-Emery Ricci tensor in terms of a suitable vector field $X$) is a constant multiple of the metric tensor. It is a generalization of Einstein metrics which contains Ricci solitons. In this paper, we focus on left-invariant vector fields and…

Integrates quadratic Lie algebroids to Riemannian Cartan-Lie groupoids.

Paper calculates Donaldson-Thomas invariants for a specific category.

Proposes a new framework for invariant quadratic P&L predictions in option books.

The paper describes metrics on left Leibniz algebras, linking them to quadratic Lie algebras.

The first part of this paper exposits a simple geometric description of the Kirby-Siebenmann invariant of a 4--manifold in terms of a quadratic refinement of its intersection form. This is the first in a sequence of higher-order intersection invariants of Whitney towers studied by the authors, particularly for the 4--b…

If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a sufficient criterion (called the …

New tool helps classify invariant subvarieties in degenerations.

We show how the space of complex spin structures of a closed oriented three-manifold embeds naturally into a space of quadratic functions associated to its linking pairing. Besides, we extend the Goussarov-Habiro theory of finite type invariants to the realm of compact oriented three-manifolds equipped with a complex s…

Holomorphic vector fields on planar triangulations are linked to quadratic differentials.

A perturbative SU(3) Casson invariant $Λ_{SU(3)}(X)$ for integral homology 3-spheres is defined. Besides being fully perturbative, it has nice properties: (1) $4 . Λ_{SU(3)}(X)$ is an integer. (2) It is preseved under orientation change. (3) A connected sum formula holds. Explicit calculations of the invariant for $1/k…

New derivation shows spacetime interval is quadratic without light.

Classification of 4-manifolds with finite fundamental groups using stable homeomorphism criteria.

A new, simple method to compute a knot invariant.

The thesis examines the signature modulo 8 of fibre bundles and identifies an obstruction to multiplicativity.

The paper introduces a new invariant for cobordism classes of manifolds and extends cobordism groups.

Quadratic differentials on Riemann surfaces uniquely determine foliations.

The paper proves rigidity of Einstein metrics as critical points of quadratic curvature functionals.

New quadratic forms expand and rotate linear endomorphisms in geometric theory.

Study Alexander polynomials of modular knots, revealing finite and infinite coefficient properties.

Configurations of rigid collections of saddle connections are connected component invariants for strata of the moduli space of quadratic differentials. They have been classified for strata of Abelian differentials by Eskin, Masur and Zorich. Similar work for strata of quadratic differentials has been done in Masur and …

The paper studies new curvature properties in Finsler geometry.

In this paper, the symmetry group of a differential system of n quadratic homogeneous first order ODEs of n variables is studied. For this purpose, we consider the action of both point and contact transformations to signify the corresponding Lie algebras. We also find the independent differential invariants of these ac…

The paper simplifies hedging and portfolio allocation in markets without a risk-free asset.

For a non-uniform lattice in SL(2,R), we consider excursions in cusp neighborhoods of a random geodesic on the corresponding finite area hyperbolic surface or orbifold. We prove a strong law for a certain partial sum involving these excursions. This generalizes a theorem of Diamond and Vaaler for continued fractions. I…

The distribution of Chern-Simons invariants on 3-manifolds resembles quadratic residues.

The paper explores quadratic differentials in spherical CR geometry and their properties.

Novel link classification connects quadratic forms and knot theory.

Efficient online control algorithms for noisy systems with quadratic losses.

Theory is developed for linear-quadratic at infinity generating families for Legendrian knots in R^3. It is shown that the unknot with maximal Thurston--Bennequin invariant of -1 has a unique linear-quadratic at infinity generating family, up to fiber-preserving diffeomorphism and stabilization. From this, invariant ge…

Random walks on mapping class group lead to recurrent geodesics in quadratic differentials.

Study of zero-divisors in sedenions via determinant factorization.

According to the work of Kontsevich-Zorich, the invariant that classifies non-hyperelliptic connected components of the moduli spaces of Abelian differentials with prescribed singularities,is the parity of the spin structure. We show that for the moduli space of quadratic differentials, the spin structure is constant o…

New metrics defined in Finsler geometry with specific properties.

This paper computes the quadratic Witt groups (the Wall L-groups) of the polynomial ring Z[t] and the integral group ring of the infinite dihedral group, with various involutions. We show that some of these groups are infinite direct sums of cyclic groups of order 2 and 4. The techniques used are quadratic linking form…

The first part of this paper completes the classification of Whitney towers in the 4-ball that was started in three related papers. We provide an algebraic framework allowing the computations of the graded groups associated to geometric filtrations of classical link concordance by order n (twisted) Whitney towers in th…

Holomorphic QDs dual to Fenchel-Nielsen coords for hyperbolic metrics.

Quadratic Killing tensors on Lie groups are always decomposable.

Develops a foundational argument for Lorentzian or Euclidean spacetime geometry without light or electromagnetic phenomena.

The study classifies 1-connected 7-manifolds with torsion-free second homology.

Study quadratic one-forms on logarithmic Higgs bundles on pointed curves.

Two non-local asymptotic invariants of magnetic fields for the ideal magnetohydrodynamics are introduced. The velocity of variation of the invariants for a non-ideal magnetohydrodynamics with a small magnetic dissipation is estimated. By means of the invariants the spectra of electromagnetic fields are investigated. A …